Are infinite regresses logically possible?
Surely it's logically possible for infinitely many positive or negative integers to exist, and they represent a kind of infinite regress: for every negative integer, there's a smaller one; for every positive integer, there's a larger one. Even those who say that only potentially infinite collections (and not actually infinite collections) are possible must admit the possibility of infinite regresses of this numerical kind.
Is the positing of an infinite regress a legitimate explanation in philosophy?
I don't see why it couldn't be. It seems to me that the burden rests with whoever denies the acceptability of an infinite regress of explanations. Indeed, I think infinite regresses of explanations are unavoidable given some highly plausible assumptions.