Audi 4000 1987 Runs Good but Stalls, Starts, and Stalls

Advise needed for Stalling Audi suddenly
I have an 87 Audi 4000s 1.8L that has an intermediate stalling problem
that is very puzzling. It seems that the fuel cuts of stalling the car,

It only does it after being started and driven 3-8 miles.
It seems like the fuel delivery just stops, vehicle looses all power quickly and stalls.
If I punch the accelerator pedal all the way when it does it,
the tranny will kick down, and the vehicle will sputter along a little bit, but otherwise, it just stalls dead.
It will start up again within 2-3 seconds, and seem to run again at full power, until the problem happens again every mile or so, but it
will always start eight back up.
I can start it and let it idle for and hour, it will not stall.
Stalling happens when going different speeds, uphill, downhill,
when accelerating or coasting, no pattern here.
I have done the following recently
1. Both Fuel Filters New 2. The Fuel Pump Relay New 3. Checked all Vacuum Hoses 4. Checked Tank Vacuum 5. The Cold Start Valve is not the problem 6. Full Tune Up 7. Cat and Exhaust - All new
I think I may hear a slight intermediate whining noise if I listen carefully, may be the Fuel Pump???? Is it possible for the Fuel Pump to
work fine, until the car has been operating for a period as I detailed above.
I have read about having crap in the tank, causing this. But why would this only happen after the vehicle drives a few miles first, it never happens before it has been driven at least 3 miles, usually it happens around 5 miles.
I guess I will spend the 200 bucks for a new fuel pump, but I wanted to
throw this problem out there to see if anyone has any other thoughts.
Thanks Richard
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richardci wrote:

Yeah, after being posted five times, I think everyone's read it now.
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