Chrysler Repair: No gas into EFI after few minutes, fuel pressure regulator, fuel pump relay

Question
I have a 1985 Chrystler Laser Non Turbo 2.2.
I start it, then after a few minutes, the car dies as if all fuel has been cut off. When I opened the breather, left the car for about an hour,(its currently about 4 degrees Celcius here) and then tried starting it up, i can see gas shooting from the jet. After a few minutes the gas stops shooting from the jet and the car dies instantly. I try starting it up right away, the engine is turning over but no fuel is shooting out of the jet. I replaced the jet, the AIS, and the fuel pressure regulator. We thought it may be the O2 sensor, but when I disconnect this from the computer, the car still does the same thing. I thought that if it was disconnected the car would run, but run rich.
I thought to the in tank fuel pump might be the cause, but wouldn't this just die? And not display the symptoms like this? I don't really know how to test a fuel pump to make sure it's running while in the tank. Any idea's?

Answer
Sounds like a fuel pump in the beginning stages of failure. Next time it dies, Innediately have someone turn on the key while you perch at rear of vehicle with fuel door open listening for the hum of fuel pump if you don't hear that is more than likely your problem. I'll assume that you have checked filter and it has good flow. Fuel pump relay is possible however symptoms are not consistent with your description so I would lean towards pump in tank.
Dale