Right after you finish a puzzle rush, you can click on the puzzles that you would like to retry and do so, but if it is later, then here's what you do:
Go to the puzzles statistics page by going to your home page, then clicking on the Puzzles, and then Full Stats.
At the bottom of the page, you can look back on past Rated Puzzles, Learning Puzzles, and Puzzle Rushes
I remember stumbling upon a way to retry puzzles I have tried but failed to complete (i mean the puzzles that I wasn't allowed to retry immediately e.g. during puzzle battle or puzzle rush) but I can't find it now. In general the chess.com website has so much room for improvement in terms of the difficulty to find stuff.