One problem related to engine shut off without warning has been reported for the 2013 BMW 328. The most recently reported issues are listed below.
Travelling at 60 mph on the highway I got a message "drivetrain malfunction". Before I was able to stop, the car shut down. It was towed to the dealer and they told me the plastic timing chain cover broke off and permanently damaged the engine. It will cost me $8300 to repair. After some research, I found others have had this happen and that BMW has since changed the design.