A rook up, can black end the checks and thereby win (LiChess.org puzzle 74754)? A LiChess.org puzzle ends at this position with white to move.  Apparently, black has a win here, but running through moves with LiChess's Stockfish, I can't seem to figure out how to end the checks.

[FEN "1K6/PPPq2PP/5P2/3p4/1p2Q3/7p/8/k2r4 w - - 0 1"]


Question: Can black end the checks and win?

Maybe there's a humanly understandable reason that the checks don't end.  Or maybe the web version of Stockfish is not looking deep enough.
Looks like you are correct with your second assumption - the evaluation didn't (cannot) look deep enough. 

It's a classic application of the horizon effect. 

The white queen essentially has half of the chessboard at her disposal to give checks, while the black king has no shelter (the single rook is not enough (but moving it every now and then will reset the 3-fold-repetition countdown) and the black queen is cut off) but a lot of space to run around. The pawn on g5 will fall with check at some point and reset the 50-move countdown, too. The number of lines increases exponentially and since none of them actually changes anything significant about the position, Stockfish cannot efficiently prune any of them. Thus the search tree grows too large to process even for a modern engine on presumably good hardware.



PS: I've tried and removed the white pawns and the black pawn on g5 who look insignificant to the perpetual at first glance to reduce the number of chessmen to 7 - low enough to use Lichess' tablebase. And indeed, that position is won for black. However, this is meaningless as both sides will quickly play moves that are impossible in the puzzle position, e.g. the white queen will move to a1 and the black king will run towards e3.