Try changing the capacitor in your fan. Check the old capacitor & replace with ane with similar rating.
For example, If 2.25uF is the calculated safe capacitance that is in the fan; 2.5uF can be used in place of 2.25uF (as it is one of the closest value) can be used, without increase in temperature of the fan motor beyond its failure. The speed of fan will slightly increase with slight increase in temperature of winding. But you may find very less reduction in speed control in lower speeds.