92 camaro v6 stalling out

I have a 1992 camaro v6 rs auto, i am having a problem with it stalling out. The car usually starts up fine and will run good for a little bit. but after a little bit it starts to dog out but if i floor it, it will hesitate but then will be fine. Sometime when i am slowing down to make a turn or at a stop sign it will shut off, but it will start up fine. Also after i shut the car off i can hear the fuel pump running real rough. my first thought was that the fuel pump was going up but i put a new fuel pump in it about 8,000 miles ago. Any suggestions what may be worng?

Best suggestion is to get your hands on a fuel pressure guage and verify if the pump is going south on you. If possible, tape it to your windsheild and have someone steadily eyeball it while driving and try to simulate the condition it acts up. Pumps on these usually just die, not sputter around or give much warning. So chekcing the pressure will help you eliminate a long afternoon of dropping the tank for possibly nothing.

Might be a relay or oil pressure switch issue?