"Initial" is pronounced "inishal," so why isn't the verb "initiate" pronounced "inishate"?

You may say the word “initial” as “inishal” but that is not universal. It is peculiar to you and likely the region where you learned English. I say “initial” and “initiate” the same way, pronouncing the second “i” in both cases.

There are no rules for this except “accents differ” and “laziness is catching.” Letters get dropped out of laziness and then kids learn to talk that way and pretty soon everybody in a region is sharing that laziness and we call it an accent. People who live in Toronto all say “Toronno.” It is easier and it caught on and now it is part of the regional accent.

I think I may have found part of the answer, so I'll put in in a post here.

After posting my question, it occured to me that a possibly analogous case is preference, /ˈprɛf(ə)rəns/, where the middle "e" can be elided, and preferential /ˌprɛfəˈrɛnʃəl/, where it cannot. So I decided to look for more information about vowel elision and English stress and metrical structure.

So I looked for information about this in general and found this: Optimality Theory and Prosody, by Michael Hammond, at the University of Arizona. Here's the portion that I found helpful (some of the bolding was added by me):

Syllables are organized into patterns of alternating prominence (METRICAL FEET). In English, each foot contains a stressed syllable on the left and at most one stressless syllable on the right ([σ (σ̆)]).

[...]

Under certain conditions, a stressless vowel can go away in fast speech (SYNCOPE)

1 a. at the beginning of words:

• paráde -> práde
• Torónto -> Trónto
• Canádian -> Cnádian

2 b. before a stressless syllable

• ópera -> ópra
• géneral -> génral
• chócolate -> chóclate

3 c. before a stressless syllable before a stressed syllable

• réspiratòry -> réspratòry
• glòrificátion -> glòrficátion

Compare:

• óp(e)ra vs. òperátic
• gén(e)ral vs. gènerálity
• glórif'y vs. glòr(i)ficátion
• réspiràte vs. résp(i)ratòry

A rule-based account: Remove a stressless vowel if it precedes a stressless syllable or if it is word-initial.

Problem: the syncope rule misses the generalization that vowels syncopate only when an optimal (=disyllabic) foot would result. The two environments above can only be reduced to a single environment when the output is considered.

A constraint-based account:

                a.       STRESS: pronounce stressed vowels.
                b.       FOOTLESS: avoid unfooted syllables.
                c.       STRESSLESS: pronounce unstressed vowels.

STRESS >> FOOTLESS >> STRESSLESS

I'm not sure how exactly to apply this to the case of CiV words, but the metrical explanation seems to apply in both cases.