This verb does not occur in Attic in impf. as it seems, only in the aorist. But would the impf coincide in form with the aorist? would it be ἐπηρόμην according to the rules?
If it is true that the imperfect form is not used, then I suggest it might be because the meaning of this word excludes connotations related to continuity of action, at least in Attic. (Could it be that the ἐπί in the combination suggests just that?). Wherever such connotations are to be expressed, εἴρομαι is probably used.
Xenophon used επηρετο in his Anabasis https://archive.org/details/wrterbuchzuxenop00voll/page/78/mode/2up and https://archive.org/details/lexikonueberdie00traugoog/page/n141/mode/1up (page 254)
You are right with your constructed imperfect-form.
A question on this:
I wondered why Traut says επηρετο is Imperfect, whilst others (Smyth) say it is a 2nd Aor.
Should the Imperf. be connected to ερομαι and the 2nd Aor. to ερωταω?
The Cambridge Greek Lexicon has ἐπέρομαι Ion. ἐπείρομαι and aor.2 ἐπηρόμην, Ion. ἐπειρόμην.
Looking through the Xenophon uses (the vast majority of this form in TLG), they mostly/all seem aorist to me. Ie.,:
ἐλθὼν δ’ ὁ Ξενοφῶν ἐπήρετο τὸν Ἀπόλλω τίνι ἂν θεῶν θύων καὶ εὐχόμενος κάλλιστα καὶ ἄριστα ἔλθοι τὴν ὁδὸν ἣν ἐπινοεῖ καὶ καλῶς πράξας σωθείη. καὶ ἀνεῖλεν αὐτῷ ὁ Ἀπόλλων…
But if someone has an example that looks like it’s being used imperfectly, they should post it.
In Xenophon επηρετο must always be aorist. With ionic (επ)ειρετο (Homer, Hdt.. etc.) it’s a trickier question.
How can the aorist morphology be explained? To be a second aorist, a stem-change is to be expected. Isn‘t ηρ- just ε(augment)+ -ερ- (presence-stem)?
Yes morphologically aor. ηρετο seems to imply present ερομαι with regular temporal augment doesn’t it, while ειρετο (non-Attic) has present ειρομαι and is without evident augment. But I don’t try to explain all the peculiarities.