Lights stay on? Alternator still connected to the battery? Starter still cranks but no start? Then you cycle the key switch and all is fine?
So, what happens when you cycle the run/stop switch instead of the key switch? If that also cures it, I would be suspicious of the run/stop switch contacts or maybe the ignitor is getting confused and needs a reset.
If only cycling the keyswitch cures it, I would start by cleaning up the fuses and fusebox contacts, then start cleaning the connectors involved with the ignition wiring. This includes the wiring all the way back to the switch.
It may be that cycling the switch causes an arc across a bad contact that burns a path for the electric power, then the path heats and oxidizes to the point of opening up again.
The problem could also be not really related to the switch at all, just the time it takes to try a few things and then work the key. Like maybe a pinched tank vent hose or a loose ground.
