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 ½ 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