What year is yours?
85/86?
If yes, and you have not upgraded to 87/88 headlights, it sounds like the bumpers that cause the motor to stop running when it reaches either upper dead-point or lower dead-point are worn out. If not unplugged, it will also drain your battery, as they will continue to run, since they don't know that they have reached the end of their travel.
Fierofool is actually our resident expert on this and can give much more advice
\D