I wonder if it could be a capacitor. Some motors have 2 caps, I believe one is for starting and one for running. I had a failure of my starting cap. The saw would start turning and then die. Replacing the one cap fixed it (~ Can $10). It's been fine for about a year since. In my case, there's like 'bubbles' in the motor case where the caps are, about 1" by 2 1/2".
Caution: Capacitors can store a charge kinda like a battery. You could get a shock even with the saw unplugged. Usually the terminals are shorted with a screwdriver or something with an insulated handle, just to be sure it won't bite.