Many homeowners find that the bathroom exhaust fan was never hooked to an exhaust duct and therefore can't produce the suction required to clear moisture from the air. Excess moisture, combined with the weight of the fan on the ceiling surface, may cause the paint to peel around the exhaust fan.
An aging exhaust fan may provide enough suction to collect moisture from the bathroom but not enough to carry the moisture out of the room and through the ventilation system. Therefore, moisture may accumulate on the ceiling near the fan and cause the paint to peel.
The paint peeling around your bathroom exhaust fan may be the first indication that the entire paint job is going to fail due to an improperly prepared surface. Always use a mildew-resistant primer when painting a bathroom ceiling and don't use latex paint over oil-based paint. The high humidity of most bathrooms aggravates painting mistakes, whether the exhaust fan works properly or not.