Progressive form of "beware"
The Oxford English Dictionary writes that there are forms in which beware is inflected. For example, they write that the secondary sense is:
As an inflected verb.
1598 J. Florio Worlde of Wordes, Raueduto, bewared, espied.
1606 N. Baxter Sir Philip Sydneys Ouránia sig. Kiij, Bewaring of too hot combustion.
1669 Milton Accedence 18, I had bewar'd if I had foreseen.
1672 I. Newton Let. 29 Jan. in Corr. (1959) I. 84, I stirred them a little together, bewaring‥that I drew not in breath neare the pernicious fumes.
1700 Dryden Chaucer's Cock & Fox in Fables 253 Once warn'd is well bewar'd.
1860 R. W. Emerson Fate in Conduct of Life 41 We beware to ask only for high things.
1870 Echo 17 Oct., Showing the greatest respect‥and bewaring of the slightest insubordination.
However, the primary sense of the verb is without these inflections. In the associated OALD, they only include the non-inflected type, and say that beware is only used in infinitives. It is this sense that most people use--without adding tense endings.
The author seems to be using only this sense of the verb, and referring to it as the sense of beware. He is not wrong in that this is the sense that most people will recognize. However, this does not mean that there have never been inflections added--they just didn't catch on into popular use. Now, the secondary use listed by the OED is not likely to be found anywhere except in old quotations. Beware is "defective" because it is a verb which doesn't take inflected endings (at least, not any more), so it has turned itself into a fairly irregular verb.
One way to look at it is this: part of the meaning of the verb beware intrinsically implies a command. So it is only readily used either as an imperative (having the same form as the infinitive) or as an infinitive as part of a construction that indicates a command. For example:
Beware of the dog!
You must beware of the dog!
whereas the following is a bit odder (although it still uses an infinitive, it doesn't imply a command):
??He decided to beware of the dog.
At least humoristically, you can just about force an inflection on "beware" if you can come up with a context where a particular piece of syntax is so tied to that situation that it can "override" the constraint of the verb not usually allowing an inflection. (Put another way, you could see it as a kind of 'metalinguistic' use.) For example, consider the following exchange between a rich fusspot and her chauffeur:
-Mind that car, Jeeves!
-Minding the car, m'am!
so similarly the following just about works:
-Beware of that dog, Jeeves!
-Bewaring the dog, m'am!
But it's certainly true that "beware" doesn't ordinarily take an inflection, and even without an inflection, appears to be tied to a particular semantic constraint (command) whatever the construction.