i don't think they should do that. Most of those sensors monitor your engine and adjust your ECU accordingly - which alters the way your engine performs, but shouldn't cut if off. Most things associated with cutting of involve would include, i would assume, the main electrical system - ignition, starter, distributor, possibly alternator, or main relay. You need Fuel, Air, and ignition for a running engine and most likely you're getting fuel and air and i'm assuming you're not getting the ignition
Bad starter - won't crank, try tapping it with a hammer
Bad ignition - won't crank OR will cut off while driving due to faulty electrical issues
bad distributor - won't start or will run poorly
Bad alternator - car wont' start due to not recharging. Dimming of lights and electrical stuff in the car.
Bad main relay - car won't start, but will start 15-20 minutes later as if nothing happened. usually happens in the summer time. bad contact points
My guess would be the ignition / main relay.