I have been having a problem with my 528i.
It started to while stop running. I tracked this down to a bad ignition module. Replaced it and it started right up. The next day it tried to start it It starts right up but stalls immediatly when the key is releasted. It starts right up but stall immediatly. I have fuel pressure.
Before you dive into replacing stuff check to see if there's a dead alarm system in the car. I had one that randomly came back to life and cut power to the ignition circuit.
I've experienced your problem as well. Other issues were also present, like in your situation (ignition module). The other issues tricked me into thinking the stalling problem was related, but the ignition switch was worn out, and a new switch fixed the problem. Good luck.
