fuel problems with an Olds Cutless Supreme

I have a 94 Olsmobile Cutless Supreme and the fuel pump seems to stop working when the car has warmed up. I'm not sure if it is the fuel pump, the fuel pump relay, a short somewhere, or something that I'm not thinking of. It doesn't stop everytime but it seems to be getting progressively worse. I pulled out the relay and heated it a little with my lighter but that didn't seem to make it stop. The car runs fine while it's running but as soon as I shut it off, the pump won't hum and start up. I thought the pump just died and quit working, but I'm probably wrong. The pump was replaced about 3 years ago, when the car was my mom's. If someone can give me an idea, I would greatly appreciate it. I just don't want to start blowing money without a better idea. Thank you for your time. Nate

You are not really stating a problem.
Once the system is pressurized the pump will not run on startup.
Once the system has depressurized they when you turn the key you will hear the pump run for five seconds.

Any good manual will tell you how to test the pump. There is a wire under the hood that is just hanging there unattached to anything, you ground it and that will force the pump to run.