In that case it can very well be the capacitor.
I never opened the case of the feeder auger (that one part never broke...) so I not sure what type of motor it is. Since it is a single phase AC motor it can only be of two types, either one similar to the fan motor
http://www.pelletsbutiken.com/86-thickb ... x-20kw.jpg, which does not have a capacitor at all (the thick copper wire that runs through part of the stator fills the same function, sort of) but that's a bit unlikely. The more likely motor type requires a capacitor either looking like this:
http://www.pelletsbutiken.com/sv/kmp-ka ... or-k6.html or like this
http://www.hedestoker.dk/3631_500_konde ... scotte.jpg, to start. It should be easy to replace yourself, unlikely but possibly requiring a soldering iron, but you of course have to find a matching one.
Even before switching capacitor I would check with an ac-voltmeter that there is 230V at the feeder connector when it should be running, to rule out some kind of intermittent fault on the circuit board.
Another possibility could be that the gearbox has dried out and jammed, I guess it is not totally unthinkable that it could be more jammed when cooled down after a stop, and if the motor manages to get it going at startup then it loosens up a bit when warming up so it keeps running until the next stop.
10 years with a KMP without troubles! You should get a medal!!

(I was probably asking to much of my poor px20, 20kW is the absolute minimum that my house requires, so it had to do more work than it could handle)
Termax 25Cr med spaksotning, Bio Comfort + lambda + kompressorrengöring, 10m skorsten med 125mm insatsrör. 8t bulkförråd. Matene vertikalskruv. https://github.com/motoz/PellMon open source pelletlogger