What brand engine do you have?
Loose wire in the wiring harness to the engine? That seems the usual suspect for an intermittent problem like this. I seem to recall some thread about an inline fuse holder in the engine compartment. The next most likely is either the ignition switch or the wiring under the dash to the ignition switch. Quite a few poorly crimped spade terminals there.
Is the low oil pressure shutdown wired on your engine? That could be a source of the problem, but unlikely. It doesn't come that way by default; positively a crime in my book, PT should have at least wired it to a buzzer.