[40cpe]

It sounds like a connection is tight enough to run the things you turn on up to the time you turn on the headlights. First check that all your ground connections are tight and clean, as in no paint under the connections. If the problem persists check along the wire that feeds into the car from the battery/solenoid for loose connections. The next time it shuts down feel along all the cables and wires for hot spots at connection points.