Doesn't sound like anything in the starter circuit since it gets going momentarily. Once it's up to speed that circuit is disconnected by the centrifugal switch. Sounds like a flaky thermal switch because you said it's a problem on hot restarts and it needs to cool down to work. On that pic the thermal switch is mounted at top center on the back plate. Just above the gray centrifugal switch spring. If you have a voltmeter you can measure across the contacts when it has quit. If you see anything other than about zero volts it's open. Cheap and easy to replace.
Al

http://www.poolforum.com/pf2/showthread.php?t=4800