Prefix "a-" in abash, abeyance and agape

Why do the three words mean so differently, given that they basically have the same prefix "a-" and root "gape"? I haven't understood yet, but the above is what I have found.

Semantic shifts can be one of the trickiest and most difficult-to-nail-down aspects of language evolution. There is no real way of answering the question ‘why’ about it—but it is often possible (with a bit of tinkering) to answer the question ‘how’.

Agape

‘Agape’ is a formation made within English itself. The prefix a- is quite productive in English, used to denote adjectives and adverbs that describe some state, manner, or activity (‘asleep’, ‘aloud’, “There she was just a-walkin’ down the street”). Its origin is as an unstressed reduction of the preposition ‘on’.

‘Gape’ is a common enough word in English, and it needs no further explanation, really. ‘Agape’ as a whole is also quite self-explanatory and basically means what it looks like. Its semantic shift is more or less nonexistent.

Abash

As you have correctly identified, this comes from the (Latin) prefix ex- plus a verbal stem meaning to gape or to yawn. Ex- in this particular word does not really have its most common meaning of ‘out of’, but is rather an intensifier, just like per- (literally ‘through’) and its Germanic counterpart, (English) for-, so often is.

In other words, abashing someone really means something like ‘pergaping’ or ‘forgaping’ them—to make them stand there with their mouth utterly open, dumbstruck. It is not hard to see how the modern meaning of the verb has developed from this.

Abeyance

This word has the same gaping root (*bay-/be(y)-) as the previous one; but in this word, the deceptively similar a- prefix is quite a different one: it is the variant of the (Latin) prefix ad- regularly found before b, so it’s really ‘adbeyance’ in the underlying form (similarly, ‘abet’ and ‘abate’ are underlyingly ‘adbet’ and ‘adbate’), or ‘gaping towards [something]’.

This is the word that has the most winding history of the three. The original meaning of ‘gaping towards’ something is to be eagerly desirous of it, a meaning that makes a good deal of sense (similar to how you can be ‘gasping for’ something). It was apparently especially used of someone who desired or expected to receive property (for whatever reason). From there was formed the noun (Old French) abeance (Anglo-French abeiance), which meant something like ‘the condition of someone who’s expecting/hoping to receive property’, in which sense it was used in French law.

When the word joined English, a somewhat odd development took place: it started to be used instead of the property that the person was expecting/hoping to receive. In a legal sense, that property would obviously usually be temporarily without an owner, which is what gave the abeyant (in the former sense) person hope/expectations of claiming it. So the English went from saying that the person was in abeyance of the property, to saying that the property was in abeyance because someone was expecting to receive it.

Thence came the current legal sense: “the position of being without, or waiting for, an owner or claimant”.

Of course, when property has no owner, it in a state of limbo, as it were, and this sense of being somehow ‘put on hold’ was then generalised to other, non-property-like, things, to give the current sense of being simply ‘suspended’ or ‘on hold’ in general.

The prepostion a- in agape serves the function of reinforcing the present participle form of the verb stem gape (just as in ablaze) - giving the sense of adding on (on gape) - thus turning the verb stem into an adjective (or an adverb).

The preposition a- in abeyance serves a similar reinforcing function and is cognate with ad- (with the first consonant being assimilated during the conjugation). The suffix -ance turns the stem into a noun form.

The prefix a- in abash, on the other hand, is a mutation of es- from ex-. Ex- here still means out of but is used here in the interjectory sense of completely, utterly or thoroughly expressing astonishment (just like the intensive prefix in aghast). Since the prefix serves merely an exclamatory function the stem retains its verb form.