Preventative vs. preventive
Solution 1:
These two words have come into being because there is arguably an -ative suffix in addition to an -ive suffix. The reason that -ative is emerging as a suffix unto itself is because of a high occurrence of -ate verbs (differentiate, alleviate, demonstrate), leading to a high co-occurrence of -at-ive words. (This is similar to how the -ical suffix emerged through the glomming together of -ic and -al, and how -ation has emerged from -ate and -ion.)
Thus, we have two fairly similar ways of constructing these types of adjectives from verbs. For many words we just use -ive, and for many -ative words there is also a corresponding -ate verb. But, there are some common -ative adjectives for which there is no intervening -ate verb. OED mentions authoritative and qualitative as examples. There's also argumentative, augmentative, and so on.
The OED says that preventive is the earlier form and preventative is later, but the citations show both of them coming around in the 1600s and first citation of preventative being just 30 years later than preventive. So, agreeing with your etymological sources, both have been around for, more or less, an equally long time.
With this information, it is hard to justify any prescriptive advice that says that only preventive is correct. This is not backed up by current usage, history, or even grammar (unless e.g. authoritative is wrong).
Your World Wide Words link makes an interesting observation; perhaps there is a prosodic influence, where the syllable-stress pattern might encourage -ative, even in certain cases where there is no -ate form. Without doing an in-depth analysis of -ative words, it's tough to know for sure.
There could be regional differences in what is preferred, but I couldn't find any hard evidence one way or the other. (I know I say preventative.)
Solution 2:
Webster's Dictionary of English Usage (1989) includes this discussion (part of a longer comment) on preventative versus preventive:
You may wonder how preventative came to be objected to. The earliest attack is in [Richard Meade] Bache 1869 [Vulgarisms and Other Errors of Speech]; he said that there was no such word. Bache's book was one of those used by [Alfred] Ayres 1881 [The Verbalist], who also criticized preventative. From Ayres it went to [Frank] Vizetelly 1906 [A Desk-Book of Errors in English], [Ambrose] Bierce 1909 [Write It Right], [H. N.] MacCracken & [Helen] Sandison 1917 [Manual of Good English], and [Charles] Lurie 1927 [How to Say It]. [Henry] Fowler 1926 [A Dictionary of Modern English Usage] picked it up too, and so it has gone right down to the 1980s. A couple of commentators—[Bergen] Evans 1962 [Comfortable Words] and [William] Watt 1967 [A Short Guide to English Usage]—realize that preventative is acceptable. Probably none of the recent objectors realizes that his opinion goes back to Bache 1869. But the moderns do not claim that preventative is nonexistent anymore; nowadays they say it is wrong because it is "irregularly formed." That is not so, of course. It is formed in the same way as authoritative, quantitative, normative, talkative, and other words to which no one objects.
The same comment appears in the (very slightly) updated Merriam-Webster's Dictionary of English Usage (1994).
But whatever the validity of preventative as a word may be today, the notion that disapproval of it originated with Bache's 1869 book is demonstrably wrong. In fact, the earliest such instance that I'm aware of occurs in the first Merriam-Webster edition of An American Dictionary of the English Language (1847). There you'll find regular-size entries for preventable and prevented:
PREVENTABLE, a. That may be prevented or hindered. Reynolds.
PREVENTED, pp. Hindered from happening or taking effect.
And between these two entries, in smaller type, this bracketed note appears:
[PREVENTATIVE is a gross blunder.]
Though the version of the relevant dictionary in Google Books is dated 1850, that edition was first published in 1847 (I have the 1852 version), which makes its denunciation of preventative 22 years older than Bache's.
Also in 1847, a similar criticism of preventative as a noun appears in Seth Hurd, A Grammatical Corrector, citing as authority an undated edition of Worcester's Dictionary:
PREVENTATIVE, for preventive ; as, "Industry and frugality are the surest preventative against poverty."
The spelling of this word with an a has become a common error.
"PREVENTATIVE, n. That which prevents : incorrectly used for preventive." WOR[CESTER'S] DIC[TIONARY]
[[UPDATE (8/23/2017): The dictionary Hurd has in mind appears to be Joseph Worcester, A Universal and Critical Dictionary of the English Language (1846).]]
With regard to the historical legitimacy of preventative, I think it's somewhat misleading to focus on the fact that its first known occurrence is just 30 years younger than the first known occurrence of preventive. The latter term appears (both as a noun and as an adjective) in every dictionary I've consulted, starting with Samuel Johnson's Dictionary of the English Language (1756), and ranging through the various nineteenth-century editions of Webster's (1806, 1828, 1840, 1847, 1867, and 1890) and the Webster's Collegiate series (1898, 1910, 1916, 1931, 1936, 1949, 1963, 1973, 1983, 1993, and 2003). In contrast, preventative makes its bracketed debut in the 1847 Webster's and then reappears in the 1864 Webster's with this full-scale entry:
Preventative, n. That which prevents;—incorrectly used instead of preventive, q. v.
This dictionary appeared five years before Bache's book. The entry for preventative in Webster's International Dictionary (1890) is identical to the one that appears in the 1864 dictionary. Webster's New International Dictionary (1910) updates the entry to read as follows:
preventative, n. That which prevents;—an unnecessary and irregularly formed doublet of preventive.
The first and second editions of Webster's Collegiate Dictionary (1898 and 1910) show no such disapproval, despite being based on the 1890 Webster's International:
preventative, n. A preventive.
But the Third (1916), Fourth (1931), and Fifth (1936) Collegiates omit preventative altogether. The term reappears in the Sixth Collegiate (1949), with the old cautionary note restored (and for the first time with acknowledgment of the word's adjective form):
preventative, n. Preventive;—an irregular formation. —preventative, adj.
Finally, the Seventh Collegiate (1963) removes the stigmatizing "—an irregular formation" from the definition; and for the past 50 years, preventative has enjoyed equal status with preventive in Merriam-Webster's estimation.
Returning to the coverage of preventative in Webster's Dictionary of English Usage, it seems not at all unlikely that early grammar commentators relied as much on Merriam-Webster's hostile view of the term from 1847 through 1910 as on Richard Bache's hostile view in 1869. Similarly the "moderns" who criticized the term in more-recent times as "irregularly formed" might have found their opinion comfortingly corroborated in Merriam-Webster's Sixth Collegiate, which was the Collegiate Dictionary of record for the years between 1949 and 1962.
As for the WDEU's assertion that preventative is just as regularly formed as authoritative, quantitative, normative, and talkative, the author of that statement neglects to observe that those four terms are adjectives that lack an earlier, identically spelled noun form and consequently do not owe their existence to it; historically, the criticism of preventative as "irregularly formed" referred to preventative as a noun (which was the only form of the word that Merriam-Webster's Collegiate Dictionary series acknowledged until 1949). A better example for the WDEU's purposes would have been recitative (from the Italian recitativo), which appears as a noun in Johnson's 1756 dictionary and in all Webster's dictionaries, and as an adjective in Webster's 1828 dictionary and all subsequent ones. But whether the noun recitative establishes a regular pattern of formation for the noun preventative—a word not derived from Italian (the corresponding Italian noun, according to Google Translate, is preventiva)—seems at least debatable.
Follow-up: What did critics mean by 'irregularly formed'?
Seven months later, it occurs to me that the WDEU may simply have misunderstood what earlier Merriam-Webster lexicographers meant by the phrases “irregularly formed” and “irregular formation.” The author of the WDEU article seems to think that the criticism is specifically about attaching the ending -ative instead of the ending –ive to preserved roots that end in the letter t.
But if that were so, why didn’t those lexicographers attack the word representative, too? It was certainly available for criticism: The Eleventh Collegiate reports that the word has been around as an adjective since the fourteenth century and as a noun since 1635.
Either representative owes its immunity from criticism to the laughable inconsistency of nineteenth- and (pre-1963) twentieth-century language experts, or those experts were applying a different notion of “regular formation” from the one that the WDEU attributes to them. The latter possibility seems more likely to me.
What would their notion have been, then? My guess is that they considered a group of words to be regularly formed if certain members of the group maintained consistent endings. Thus, for instance, each of these six word groups would qualify as regularly formed:
collect (v.), collection (n.), collective (adj.) collective (n.)
compete (v.), competition (n.), competitive (adj.)
prevent (v.), prevention (n.), preventive (adj.), preventive (n.)
relate (v.), relation (n.), relative (adj.) , relative (n.)
represent (v.), representation (n.), representative (adj.), representative (n.)
sedate (v.), sedation (n.), sedative (adj.), sedative (n.)
What makes each of these words regularly formed within its word group isn’t that it follows some blanket rule about adding –ive instead of –ative or –itive to certain noun and adjective forms; it’s that the same decision about how to handle those endings applies to all relevant forms in the specific group.
In other words, once representative is established as the preferred adjective form in the represent word group, the later regular noun forms are representative and representation; and representive and represention are irregularly formed. Likewise, if preventative were the first preferred noun form for the prevent word group, the later regular noun and adjective forms would be preventation and preventative, and prevention and preventive would be irregular forms.
I don't claim that this line of reasoning is persuasive or that it proves that preventative is “irregularly formed” as a matter of modern grammatical interpretation. I merely observe that such an understanding of “irregular formation” is internally consistent (at least in the subset of examples I’ve listed above) and that, as a basis for analysis, it is far more descriptive than prescriptive.
[[Update (5/19/2019): Site participant sumelic, whose knowledge of linguistics far, far exceeds mine, offers the following note about the meaning of "regular formation" and "irregular formation," posted as a comment beneath this answer:
I believe the "irregularity" of the formation is based on Latin forms of verbs. Usually, "-at-" occurs in Latin verbs of the first conjugation, as part of the past-participle or supine stem. E.g. "represent" comes from Latin "representare", supine "representatum". But "prevent" comes from a Latin word of the fourth conjugation, "praevenire", supine "praeventum".
I thank sumelic for providing this explanation.]]
A note on 'preventive' and 'preventative' in dictionaries before 1850
My original answer didn't pursue dictionary coverage of preventive and preventative into the period before Johnson's A Dictionary of the English Language (1756). But there are a few earlier dictionaries online, so I decided to see how they deal with the two words.
Edward Phillips & John Kersey The New World of Words: or, Universal English Dictionary, sixth edition (1706) has this brief entry for preventive (and no mention of preventative):
Preventive, that serves to prevent.
Two years later, John Kersey, Dictionarium Anglo-Britannicum: Or, A General English Dictionary (1708) has the identical entry for preventive (and again nothing for preventative). And the same treatment also occurs in Kersey & Phillips, New World of Words, Seventh Edition (1720).
Nathan Bailey, An Universal Etymological English Dictionary, second edition (1724) retains the Kersey & Phillips definition of preventive (and ignores preventative), but adds the following brief etymological note:
PREVENTIVE, {Prevenant, F. of Prævenire, L.} that serves to prevent.
Bailey repeats this treatment of the word in, for example the fifth edition (1731) and the fourteenth edition (1751) of the Universal Etymological English Dictionary.
The one great exception to the among pre-Johnson dictionaries in including preventative is Thomas Dyche & William Pardon, A New General English Dictionary, third edition (1740):
PREVENTIVE or PREVENTATIVE (A.) that has the power or faculty of hindering or keeping back any thing.
The word also appears in that dictionary as part of the definition of restrictive:
RESTRICTIVE (A.) preventative, hindering, binding, making hard or costive.
while preventive appears as part of the definition of obstructive:
OBSTRUCTIVE (A.) of a hindering or preventive nature.
This dictionary offers the same relevant entries across many editions, including the eleventh edition (1760) and the fourteenth edition (1771). Perhaps the most curious thing about this treatment is that Dyche & Pardon identifies preventive and preventative exclusively as adjectives (not as nouns). Merriam-Webster doesn't list the adjective form of preventative in its Collegiate Dictionary series until 1949.
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Shifting now to the Johnson and post-Johnson era, we find two entries for preventive (and none for preventative) in Thomas Sheridan, A General Dictionary of the English Language, volume 2 (1780):
PREVENTIVE, a. Tending to hinder; preservative, hindering ill.
PREVENTIVE, s. A preservative
Sheridan repeats this treatment in, for example, his Complete Dictionary of the English Language (1790), and the same definitions are carried over to Stephen Jones, Sheridan Improved: A General Pronouncing and Explanatory Dictionary of the English Language (1798) and John Walker, A Critical Pronouncing Dictionary, and Expositor of the English Language (1807) has these entries:
PREVENTIVE, a. Tending to hinder ; preservative, hindering ill.
PREVENTIVE, s. A preservative, that which prevents, an antidote.
Those entries reappear as late as the 1823 edition of Walker, still with no mention of preventative.
Encyclopædia Perthensis; Or Universal Dictionary of the Arts, second edition, volume 18 (1816) freshens the definitions of preventive a bit and cites three early occurrences of its use, but again omits preventative altogether:
PREVENTIVE. adj. {from prevent.} 1. Tending to hinder.—Wars preventive upon just fears are true defensives. Bacon. 2. Preservative ; hindering ill. It has of before the thing prevented.—Physick is curative or preventive of diseases ; preventive is that which, by purging noxious humours, preventeth sickness. Brown.—Procuring a due degree of sweat and perspiration, is the best preventive of the gout. Arbuthnot.
PREVENTIVE. n.s. {from prevent.} A preservative ; that which prevents ; an antidote previously taken.
The earliest dictionary I've been able to find that lists preventative as a noun is Richard Jodrell, Philology on the English Language (1820):
PREVENTATIVE, & PREVENTIVE, n. A remedy tending to prevent disease. [Cited examples:] The powdered root has been given in doses of ten or more grains, as a preventative after the bite of a mad dog. Pilkington, View of Derbyshire, vol. i, p. 356, ed. 1803. Preventive, that serves to prevent. Phillips, New World of Words.
Jodrell puts an asterisk before the word PREVENTATIVE because Johnson never included the word in editions of his dictionary:
The Asterisk denotes words not inserted by Dr. Johnson himself, in the last Folio Edition, which he revised in 1783.
Here is an Ngram chart that tracks the frequency of use of preventative (blue line) and preventive (red line) in the Google Books database across the years 1700 through 1900:
Conclusions
Unquestionably, preventative has been in continuous and significant use for a long time, especially in medical texts, but also in such settings as The Federalist Papers (where Alexander Hamilton comments "if the defence of the community, under such circumstances [a rebellion or invasion], should make it necessary to have an army, so numerous as to hazard its liberty, this is one of those calamities for which there is neither preventative nor cure"). Just as clearly, however, preventative is historically a newer and much less common word than than preventive, received far less attention from lexicographers during the period from 1708 to 1963, and for much of that time endured hostility from dictionaries and grammar commentators.
For more than fifty years, Merriam-Webster has treated preventative and preventive as equally legitimate words, and there is certainly far less stigma attached to preventative today than was the case a century ago. But fair or unfair, its history of dubious status is on record, and memories of an unsavory past can cling to words long after the force of the original criticism has dissipated.