1988 325I question

Hello,
I have a 1988 325I convertable with 75,000 miles. I am looking for some help with what I believe to be a electrical problem. Every now and then the car dies while im driving, some times while its idling some times when im doing 40mph and will not start again. The car has spark but im guessing no fuel. If I take the fuel pump relay out and put a jumper wire between terminals 30 and 87, turn the key to the second on possision I can hear the fuel pump running. After letting it run for a few seconds I turn the key off, pull the jumper and put the relay back in and the car will start(some times I have to do it a few times). I have replaced the fuel filter and Idle Speed Regulator. I checked the voltage to the Throttle Position Switch and to the fuel pump relay and both were good. I also checked the relay for continuity and its good. I have thought about replacing the fuel pump but I dont think it will help since its so random when it happens(and it works when the jumpers in). What other components would you suggest that I check?

This is my first BMW and Im not the best mechanic but am willing to give any advice a try
thanks for any help you can provide.

Have you inspected inside the tank to see if anything is blocking the fuel pump from sucking the fuel out? There is also a filter on the end of the fuel pump that may be really dirty but I dont think that would stop the fuel flow.

I had a fuel pump that would work that way every once in a while. One minute, it works, next it doesn't. I finally just got a used one and it worked fine. You can get a used fuel pump for $40 to 50...shipped, maybe even cheaper in your area.