Welcome. My name is ***** ***** would be glad to assist.
Unfortunately, the only way to work on one to be able to access the fixture on the bottom of the fan to get to the wiring area.
A tester would be in order to measure the voltage tot he wires on the lighting fixture.
The fixture works off 2 wires and then with the testing, can find out if the wattage limiter is failing.
That is the most suspect item at this time.
Wattage limiters are required by the government to limit the bulb size in fans used. They shutdown power when they sense too much wattage.
In your case though, I suspect it is failing on and off and causing the issue, not because of too much being used.
That is the problem with these units, they fail very easily because their quality of production.
If you can get access and remove the light kit to access the wiring, we can test the wiring to that point.
Let me know and we can continue,