There are several time limits, but I believe that one of them stops when pulling back from the gate. i.e. once the the plane is moving, they're granted several

There are several time limits, but I believe that one of them stops when pulling back from the gate. i.e. once the the plane is moving, they're granted several X more hours, but if they haven't left yet, then they've timed out. So the arriving crew may plausibly be usable upon arrival, but a few minutes late may be all it takes to time them out. I've been on a delayed plane where one of the pilots timed out while sitting at the gate, so we had another second delay finding another pilot.