fuel pump?

I have difficulty restarting my Ford Taurus after I shut off the engine for only a short perid of time (less than one hour). Usually I need to wait for about two hours or longer, and it will restart. Two days ago, it was towed, and my mechanic hooked it up with the machine and tried to get a diagnosis but could get nothing, but the fuel did not come out, either. He said the fule pump needed to be replaced. The car sat at the garage overnight, and everything was fine again the next day. He said it's weird, and the coil temperature is ok. He also said it's possible that the fuel pump is at its last leg, and sometimes it works, but sometimes does not, and it has nothing to do with the coil temperature. Any ideas or suggestions what I should do? Thanks. Lee