Daytime running lights go out 92 Grand Prix

Most commonly this is caused by the head light switch. They have an auto-resetting circuit breaker that can develop arced contacts. That resistance causes heat buildup which helps the circuit breaker to trip. High beams draw higher current which makes the circuit breaker trip sooner. The missing clue here is the lights should flicker back on intermittently. Related to this is overheated connector terminals on the switch. Look for black terminals and a melted section on the connector body.

Since the low beams appear to always work, that would have to rule out the head light switch and point to the multi-function switch. Those don't incorporate a circuit breaker but they can develop arced contacts and overheated terminals. Start by checking the connector on that switch. If you don't see anything obvious, voltage measurements will help to isolate the break in the circuit.