The obvious fix is to switch to higher precision at some zoom level, but that can be much slower and less well supported by graphics cards. To zoom infinitely deep would require arbitrary precision arithmetic, which is very slow to implement in any reasonable way on graphics cards (all those "super-deep" zooms you see on Youtube are made with CPU's and are not rendered in realtime). You could settle for some "nice" precision like, say, 256-bit arithmetic, and optimize the add/multiply operations on the graphics cards, you'll eventually reach a limit but it should still be realtime at that precision and you'll be able to zoom much further in.
There's also some advanced techniques to get more out of 32-bit floating-point precision, utilizing things like perturbation theory, but that can be tricky to implement (worth looking into). But at the end of the day if you truly want infinite precision you pretty much need to resign yourself to the fact that the further you zoom in, the more precision you need, and the slower it's going to be, so CPU's + offline rendering are king for really deep zooms.
