Car stalls while driving

My car starts fine, am able to drive it for 10 - 15 minutes (approx 5 to 10 miles) and then the engine just dies. Car is going on momentum, SES and CEL comes on, the security light flashes 3 times and then if I press the accelerator, the car jerks back into power and continues on till it stalls again which could be another 5 to 15 minutes, or on some occasions runs fine till next day when it repeats. Dealer pulled code P1629 and said BCM needs to be replaced, but say that may not solve the problem, and they would replace the ECM after that. They haven't stated what they would replace after that. Crank position sensor is okay. Another mechanic said that he does not think it could be the BCM because all the modules seems to be operating okay and communicating with each other. He found the air intake sensor (built into the air mass flow sensor) was bad and replaced it bu that has not solved the problem. He also checked the electrical harness.

My question is if anyone has an idea of what could be causing the intermittent stalling. Also, one the car has started fine and has been running (meaning that the passlock sent the correct passcode to the BCM and the BCM sent the fuel and spark enable code to the PCM), could the passlock system still shut down the engine. This would mean that the passlock is continuously moniotoring the car (not just during starting) even while driving to verify security.

Thanks for any help you can provide.