My Exhaust Fan is not removing moisture from bathroom, why?

There are a couple of reasons as to why this might be happening. See below for a couple if things to check:

1. Remove the grill cover and give your blower and motor a good cleaning. It is possible that there is a build up of dust and debris that is preventing efficient function of the unit. 
2. After cleaning the unit, try to rotate the blower to ensure it rotates freely. If it does, that is normal. 
3. Be sure to verify that there is current from the switch to the motor. 

If none of these solve the problem, it is likely a failed blower motor, which would require replacement of the blower motor to resolve.