I do sympathize with the sentiments expressed in comments here about the complexity of Greek particles. As I started looking into this I realized that there are many pieces of the puzzle that are well beyond my own Greek. However, there is a "rule"1 about whether ἂν is included or not (albeit a controverted and contradicted one), and in broad strokes it seems to me explicable by examples in a way that might resolve the OP’s persistent itch:
What does this word's inclusion tell us that the word "ἕως" does not?
The particle ἂν here shouldn't be understood on its own. It's part of a "formula" with ἕως that (arguably2) marks a usage that is distinct from the solitary ἕως. Both fall within the semantic range of the English "until", although we can understand by example several categories within this. Pausing, I quote the wise statement made by Gildersleeve2 regarding the use of categories to describe grammatical concepts:
We are all too apt to take our pigeon holes for pilgrim shrines.
Now, on to the our pigeon hole/rule: ἕως ἂν begins a subjunctive clause; ἕως begins an indicative clause.3
First realize that both the English until and Greek ἕως have two different uses — as a preposition or as a (subordinating) conjunction. For the prepositional usage see, for example, Matt. 2:25:
καὶ ἦν ἐκεῖ ἕως τῆς τελευτῆς Ἡρῴδου·
and he remained there until the death of Herod.
ἕως has an object (the death), but it does not set up a clause (i.e. there is no verb[al idea]).4 When used in this way ἕως never (as far as I know) takes the particle ἂν. The prepositional usage constitutes 108 out of the 146 uses of the word in the NT. You're interested in the other 38 instances (14 of which are in Matthew), where ἕως is a conjunction leading a subordinate clause. Within that group, we can divide them into two categories:
- ἕως + indicative verb (2x in Matthew, both without ἂν)
- ἕως + subjunctive verb (12x in Matthew, 11x with ἂν5 ).
The usage patterns:
ἕως + (usually aorist) indicative verb: These tend to occur past narrative sequences. See, for example, Matt 2:9:
ὁ ἀστήρ.... προῆγεν αὐτούς, ἕως ἐλθὼν ἐστάθη ἐπάνω οὗ ἦν τὸ παιδίον.
the star....went before them, until (ἕως) it came to rest (lit. having come, it rested, indic.) over the place where the child was.
You may be able to construe some contingency there, but it's basically just describing a temporal sequence that is not conditional from the perspective of the narrator.
ἕως ἂν + subjunctive verb: These usually describe a sequence that is future with respect to the narrator and includes an element of contingency similar to the example you ask about. For another example from the same pericope quoted above, see the angel's words to Joseph in 2:13:
καὶ φεῦγε εἰς Αἴγυπτον καὶ ἴσθι ἐκεῖ ἕως ἂν εἴπω σοι
and flee to Egypt and remain there until (ἕως ἂν) I tell (subj.) you
From the perspective of the speaker, ἕως ἂν + subjunctive describes future contingency. The state of remaining there may be ended, contingent upon I will tell you. Similarly (as well-elaborated in another answer):
οὐ μὴ παρέλθῃ ἡ γενεὰ αὕτη ἕως ἂν πάντα ταῦτα γένηται
this generation will not pass away until (ἕως ἂν) all these things take place (subj.)
The state of not passing away may be ended (pardon the double negative; preserved for parallelism with prior example), contingent upon all these things will take place.
Summary: Although both ἕως and ἕως ἂν can be translated "until", they follow distinct usage patterns. The idea of a future contingency such as Matt 24:34 is normally expressed using the latter.
- So-called by BDAG. (William Arndt, Frederick W. Danker, and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature. 3rd ed. Chicago: University of Chicago Press, 2000. ἕως, 1aβ.)
- Basil Gildersleeve, Temporal Sentences of Limit in Greek, American Journal of Philology 24/4 (1903), 388—407.
- This was alluded to in the LSJ entry included in another answer; I'm not sure how transparent that was to the OP.
- Of course, semantically these usages aren't really distinct: "until the death of Herod" = "until Herod died". See above re. pigeon holes....
- The exception is Matt 18:30,
ἔβαλεν αὐτὸν εἰς φυλακὴν ἕως ἀποδῷ τὸ ὀφειλόμενον | He put him in prison until he should pay the debt. This is also the only one of those 12 Greek subjunctives that the ESV felt required a "marked" subjunctive in English. It's within a past tense narrative but future and conditional from the perspective of the servants in the story.