An electric motor will usually give you some indication of failure - either it will stop completely - or give off a burning smell - or sparks and noise as the brushes begin to self destruct.
From what you say I would not suspect the motor and you've eliminated the switch - so there's not much left that it could be.
I don't know if these things have an over-heat safety cut out - it's possible that there is one - it will be fixed to the motor - and it could be tripping erroneously.
There could also be an issue with the power cable - if you've been tugging on it over a period of time then cut away the plug and a few inches of cable and fit a new plug - quick & cheap and it may be a fix.
Other than that I'd guess the over-heat device if there is one.
Examine the motor to see where the wires go.
Good Luck..., May 2016
