How do I script Perl to continuously run?

Avoid any terminating statements such as exit or die, handle all signals, wrap any calls which may cause termination in eval (or use one of the try/catch modules), ensure you don't exhaust the limited resources of the hardware or the limits assigned to the process by the O/S. If using threads, ensure everything is thread-safe. If you do all that and your script still fails to run continuously then you'll need to provide some more detail.