1995 Buick Park Avenue wont stay running

Once you start it runs as long as there is oil pressure if pressure is low may be the proble or a short in wiring. Check to see if the gray wire leading form oil pressure sender is sending power could be a connection problem as well so check fuel pressure relay for corrosion.

Actually the oil pressure switch is a redundant, overlapping power supply to the fuel pump in this circuit. The only way low oil pressure can cut off fuel pump power is if the primary circuit/fuel pump relay is not working and if that were the case, you would have a very hard time starting the car because you would have no prime. You really need a fuel pressure gauge to determine what this system is doing. If you get fuel pump power for 2 seconds when the key is first turned on, then you are going to have to look elsewhere for the problem. My best guess is the pump is overheating and the current draw is pulling the voltage right down to nothing.