What causes fuel pump to fail only at start up?

It's occurring more often. With ignition on the pressure builds up to 40psi, if it starts, pressure stays up (36.0psi) and the engine will run until it's turned off. If it fails to start, the pressure drops off and doesn't return for several attempts, or until I get tired of trying. Go out an hour later or the next day, it fires up. The regulator checks out, 36.0psi at idle 43.0psi throttle up. Disconnect vacuum pressure rises to 40psi. The resistance in the pump is 0.5, which is where it's supposed to be. Replaced the pump relay and checked all but one connector, E.F.I. Harness to the relay harness (F52-M36), I have no idea where that's located. When not starting, checked voltage through both pump and safety relays (11.8) in and out, connector at pump (11.8) either side of connector. I am at a loss. It doesn't seem like a short or bad pump, because it hasn't quit running yet, only has problem when starting. Any ideas? I have been searching forever on line for answers and haven't found a similar problem.