Darren
If it's a motor with a start switch, I would do this:
Next time the sod acts the goat, while it's a-buzzin, give the chuck a twist.
If it starts, it's yer start circuit. So:
Caps are usually not the culprit, in my experience, go for the centrifugal doings.
If you ever have a shufti at these cheapskate devices, you will see an unlikely arrangement of bits of bent metal and a couple of springs.
These are VERY prone to temporarily jamming up due to fretting rust on the bearing surfaces. If you find this, clean 'em off and lube with a bit of 3in1 on a matchsick.
T'other source of grief are the contacts, any 'pip & crater' they aren't usually fixable. There ain't a lot of contact alloy, if your're down to base metal, you are done for. Look at the connections on the paxolin plate that all the things attach to. Particularly the brass 'rivets' that take the phossy contact springs, I have seen a number where there have been poor grip leading to heat cycling and looseness.
Another idea I have used, good if you suspect the switch is sticking, is to get a rubber mallet, and administer a sharp wallop or two.
Or more if you're feeling particularly narky..
If it always runs OK afterwards, the windings are almost certainly OK. A dead winding is usually forever, not just for Christmas.
Just look for poor/loose push-ons etc. usual things that screw up any elec. device.
Bout it really
Dave BC
Edit No it ain't about it! Check the sliding bush on the motor shaft.

Also, when the motor stops, you can usually hear the switch click, followed by a quiet 'hiss' as the motor stops. Does it do that?