It could be that the shaft has worn into the bronze bushings making a fairly tight fit until the fan gets up to speed and the shaft tends to climb out of its worn groove. If feasible, try turning the fan upside down to see if it starts normally; i.e. so the shaft is initially only making a point contact at the bottom of the sleeve resulting in minimal initial friction. If so, maybe you can unmount the motor and turn it upside down for a few more years of service.