Use Replacement Headlight not working at the second power up

Kind of a bizarre symptom for non-hid headlamps. The fact that it has had a frontal collision leaves open some variables. More than likely, it is a wiring type problem. On the second power up, the power and ground would have to be traced back through the circuit to the source, and determine where it is being lost. On halogen lamps, they just require 12 volts to operate, unlike a xenon(hid) which requires a ballast to charge and deliver 20k plus volts to ignite the bulb. If you are on the same key cycle, and switch the lamps from off back to on, do the lamps not light, and is it both low beams?