I would think that your motor is overheating?!? most motors have an overheat cutout switch. when the motor gets too hot it is too big for the windings so to stop it jamming and catching fire, they fit a cut out switch.
when the motor cools down, it starts again.
you would need to replace the motor. if it is not old, do it under warrenty. if the warrenty has expired, appeal to Dyson saying that the motor shouldn't break down after xxx years / months.
Julian
February 2007