| when i had my 99 540ia 63000 miles i was driving and came to traffic lights and it just cut out. i tried to start it again and the engine would not start, the starter just kept kicking in. amyhow it turned out it was the fuel relay or pump, the stealer had to take out the back seats and empty the tank to fix it, the wire had come loose, i would say that this is your problem as mine stuttered before it cut out.
not sure what exact part it was but i know it was in the fuel tank.
no one has sugested this but i guess it is worth a try as your problem sounds like fuel supply
andy | 
