They usually have an over-heat safety cut-out strapped to the motor. Possibly the motor is getting too hot because of a fault or poor air flow - possibly the safety cut-out is defective and operating prematurely.
http://www.lmelectricalshop.co.uk/dyson-ydk-thermal-fuse-dc04-dc05-dc07-dc08-11-14-19-20-p-2924.html
Peccavi
June 2011
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