I accidentally made Mewtwo faint and it won't come back. I tried leaving and coming back, but it didn't work. How can I get it back so that I can catch it?
To get another shot at capturing Mewtwo, you must beat the elite four (and champion) again. This will cause Mewtwo (and other similar legendaries you may have fainted rather than caught) to respawn.
As this question notes, once you catch it, it will no longer respawn after beating the Elite Four.