Bathroom lights go off and come back on after a few minutes
if you have LED bulbs in a globe with no airflow, they can overheat. Many have a thermal shutdown feature that will turn off the LEDs if they get too hot. Once they cool down, the controller allows them to turn on again. This explains why flipping the power does nothing: they are still too hot.

Try a lower wattage bulb, a more expensive bulb, or a decorative tungsten bulb.