Just a couple of months ago, two works by the legendary Sappho were rediscovered. Indeed, ancient manuscripts are being discovered all the time.

They're gone for good, I'm afraid. In principle there's a very, very tiny chance that some might turn up in a library like the one in the Villa of the Papyri at Herculaneum; but Herculaneum is a very unusual find-spot that can't be replicated, and the bits of that library that haven't been dug up yet are likely to be more philosophical treatises rather than literary classics.

Odd fragments do turn up in other contexts too, like papyri recovered from ancient Egyptian rubbish dumps and mummy cartonnage, but 99.9% of them are tiny scraps, and most of the rest aren't much better.

Only one complete work has ever been recovered that way: Menander's comic play the Grouch (Dyskolos) -- and actually even that isn't complete; we have bits of all five acts, but there are substantial gaps. Other than Menander, the next best find would probably be the bleeding chunks of Sophocles' satyr play the Trackers; text here. Those 380 lines probably represent about a third of the play. Over the last century about 500 lines of the Hesiodic Catalogue of Women have turned up, but they're mostly snippets dotted all round the poem (which was probably about 5000 lines in total).

Small scraps are turning up all the time. Every few years, a connected passage of about a paragraph may turn up. But I fear Menander's Grouch is likely to remain a unique find.