electrical problems?.. plz help
 

I have an '87 acura integra rs 2.5l. The problem I'm having is when I keep the car idle it will shut down after the car heats up for about 10 minutes. I have noticed the water pump isn't functioning so that's my first fix buy I can't figure out what could be shutting thecar off. Also when it does start idling if you take it out for a drive the car will shut off and refuses to start up again for 10-20 minutes. It runs great when it gets going but it takes the car shutting off or me racing it as hard as I can until the pgm efi light comes on. Any help would be amazing.

Parts replaced: fuel pump, fuel filter, spark plugs, distributor, oil filter, main relay, battery, I've put fuel injection cleaner in, new coolant, new oil.