Check in this order:
1. Ground connection at the headlights (the little eyelet screwed stupidly into the chassis with no regard for the effects of corrosion). Take them both off and polish them up, and cover with antiseize.
2. Headlight switch/socket for melting and/or overheating indications.
3. Bad battery --> engine --> chassis ground connections. Hell, just making sure these are okay can make the engine perform a little better...if you consider engine control has a lot to do with the EEC's measurement of sensor voltages, that is.
I don't remember if there's a headlight circuit breaker in the fuse box, but I do know there's fuseable links powering that circuit (coming off the battery side of the starter solenoid) that could also have bad connections. These bad connections could be enough to cause excessive current and could therefore be tripping a circuit/thermal breaker.
Something's wrong somewhere; find it before it catches on fire!
