My ceiling fans stops after being on for 4 to 5 hours. Power is still on. I turn power off and back on and it runs again. Could this be the capacitor going bad?

Most motors use a start capacitor to create phase shift to get motor turning. So i would think once in motion it will continue to turn.
Now having said that what keeps fan turning! The system relies on electromagnets which pull the motor into next section ( think of a cut pie with separation between slices).
So what can cause this sequence to stop.
1. You have a quick loss of power.
2. You have a motor thermocouple (prevents burn out at a raised temperature)
since it restarts, although you mentioned after 4-5 hours of running, there was no mention how long it sat off. I would think this is not problem.
Power loss! Do lights flicker when AC comes on?
is the on off switch a pull chain or wall-switch?
If a flicker then power might be interrupted just as the fan motor has rotated in to pie slice dead zone. Which means slim that all flickers would effect, but could.
A wall switch can build up resistance or have poor contacts that by way of vibration lose power for a split second.
Remember cap.is used to start, so follow the path for quick power loss.
Also check connections at fan to wiring, a loose connection can open due to vibration, then settle down when off