Most ceiling fans and table fans designed for household use, eventually slows down before completely failing to work.
By close observations I found these fans are using capacitor-split-phase motor and failure of the motor is electrical and not mechanical such as ill bearing etc. When the capacitor feeding one of the two coils of the motor get weak (dropping capacitance), the motor not able to develop and maintain the torque needed to sustain rotor speed.
The type of capacitor used in this fans are generally Metallized Polyester Film. Why this capacitor fails?
Capacitance is depends on dielectric constant of the insulation of polyester, thickness of that insulation film and total area of the metallized surfaces.
I belive the drops of capacitance is due to somehow the metallized surface effective area drops due to discontinuity develops within the rolled film. Polyester is stable thus it's dielectric constant or its dimension will not change over time.
If the cracks that cause discontinuity of metallic surface on the film is what cause the drop of capacitance, why it happens?