I should take some picture of the internals of those motors sometime, since I took a few of them apart recently to Frankenstein together one good one. There are two gears inside that tend to strip, and the inside of the upper motor casing also has stops molded into it that will only allow the motor to turn so far in either direction. The cover, which is what the arm fits onto, also has ridges for the same purpose. What seems to happen is that first the arm breaks, which makes the stops on the cover non-functional. Then the gears inside hit the internal cover stops, and slowly crack the cover's plastic and strip their teeth off. When all that happens, the motor is free to turn continuously, which eventually burns out the resistor. When you open most of these motors, you'll find nylon strips, which were the gear teeth, and chunks of black plastic, which were the gear stops, floating around inside the case. If you're really unlucky, the motor resistor will be burned out, too. If a new motor wasn't $200, plus the cost of a new arm, I'd never recommend trying to fix one, but they are, so fixing one becomes a lot more economical. I would recommend the Skandix kit that eEuroparts sells, but they jacked up the price by over $20 sometime in the last week. $76.99 seems like highway robbery for a cheap plastic arm and two nylon gears.
https://www.eeuroparts.com/Parts/62421/Air-Circulation-Repair-Kit-1030209/