Beyond attempting to pull codes to try to detect the problem, ask about attaching a diagnostic data recorder to the engine. ( a shop tool recorder, temporally mounted in the passenger compartment - usually ) Drive around as long as it takes for the car to exhibit the problem and then back to the dealer.
You may have to call different dealers or shops to find out more about such a method to diagnose.
If the car is still under warranty, have the complaint documented.
Also when the car stalls notice if the tach drops instantaneously to zero, or if the tach needle falls incrementally to zero. Instantaneously usually means electrical, incrementally usually means mechanical - like a fuel clogging issue.
Sounds simple, but the noise from the rear - make sure your battery is mounted securely.