It happens to AI cars, as well as when player is a gunner or a passenger. It happens to cars in group and lone vehicles. Issuing stealth (silent) mode order doesn't help.
One repeatable observation about the frequency or cause of this behaviour is that the leading car in a group suffers the issue, while subordinate vehicles turn their engines off after a short waiting. Lone vehicle doesn't turn the engine off, like if he was a leader of a nonexistent group.