Someone mentioned the run capacitor and he is probably correct. If the capacitor fails, the motor will draw high amps and go out on internal overload. these motors have sleeve bearings and unless they are in really bad condition, they normally won't stop the motor from running, though they could get pretty noisy. the fam motor is fairly easy to replace even for a first timer though the unit is a bit easier once its on the roof. If you decide to upgrade to a 15,000 BTU check the the current draw rating before you purchase. Most 13,500 are on a 15 amp circuit and most 15,000's require a 20 amp circuit. Don't worry about your gen handling it. 6.5 kW can handle far more than even 2 15's will put on it
