Bumping the starter as the motor stall sends 12 volts (instead of 9 or so) to the coil, if only for a brief moment.
Try this: Rig up a jumper from the battery terminal cable on the solenoid (always 12 volts) to the + terminal on the coil. Use alligator clips for both ends. When the motor dies, hook up the jumper and fire it up again. If she keeps running, you have one of the following problems:
1. Bad coil
2. Bad ECU (module)
3. Bad ballast resistor (break inside you can't see).
Jeff
"...reality is not nearly as lovely as the world of Liberal Land. No wonder so many people want to go there." - Tom Sowell