Each trap on a Venus Flytrap can only snap so many times. This is regardless of whether that particular trap has caught prey or not.
This is due to an in-built damage reduction strategy the plant applies. After a certain number of closures the plant will retire that particular trap in order to afford energy to grow a new trap.
The reason that traps can only close a certain number of times, and not continuously, is because of the ‘acid growth’ stage in leaf closure. After several closures, the cells of the plant are as elongated and stretched as they can get or may have become damaged from wriggling insects or other factors. It is sensible for the plant to grow a new trap which is perfectly healthy in order to maximise the chance of a successful capture.
When a trap is retired is does not die. The lobes fold backwards to form an almost flat surface. Any coloured areas of the leaf will usually turn green. The plant then uses this leaf as a normal photosynthetic leaf to collect as much energy as possible to grow more healthy future leaves.
You should not really cut these leaves off as they do provide a lot of energy for the plant (although they arn’t as pretty as a standard leaf and trap).