Most dictionaries of phrases seem to agree that this phrase means: frequently; repeatedly; over and over. Something happens once, and then again, possibly many times.
Now if you have a bee in your bonnet, as I do, about time, you may wonder why the word ‘time’ needs to appear in this context. ‘Once and again’ or ‘again and again’ express the same thing, without introducing the tricky notion (to me, anyway) of the same ‘bit’ of time coming back again.
If time does nothing, as I perceive it, then it can’t do it again.
If something happens again, it happens again. The fact is that we’ve been schooled to use ‘time’ as meaning a sort of medium in which events float, and to see those events as preceding/following each other in the same way that two vessels on a river or vehicles on a highway do.
Time doesn’t come again because it’s not going anywhere.