Well, my understanding is that the three prong pressure switch uses one of the pins for the gauge and the other for the PCM. If the PCM doesn't detect oil pressure after so many seconds it switches off the pump via the ground to prevent damage. If that circuit in the switch is malfunctioning when warm it could potentially cause a hard/no start condition. You could test the ground to the relay by running a small wire from the PCM grounded pin of the relay to the test lead on a multimeter to verify voltage or lack thereof when the hard start/no start condition is present. You could also bypass the relay with a jumper to see if it starts. The other option that I haven't seen mentioned is a power/ground issue at the pump. Bad connections caused by corrosion are usually exacerbated by heat, which only become worse as current flows through the connection creating more heat. Solution is to check voltage to the pump when the hard start/no start condition is present. Drop of more than .5V is unacceptable and can cause fuel pressure issues. The best solution is to replace the pump harness and upgrade the power and ground wires with one of a heavier gauge to minimize voltage drop. This will also extend your pump life by preventing a low voltage condition which can overstress the pump and burn it out.