Bathroom switchhas delays
The same thing happens to the bathroom fan in my office building. The problem is the fan itself; the grease in the bearings has degraded, and the motor is sticking. Without air flow, the motor heats up, and eventually the grease thins enough to let the fan turn again.

I'd replace the fan; it may be a fire hazard. (Yes, I'm working on my office landlord to get this done as well...)