dyson root cyclone turns off?

Either a broken conductor in the cable near the plug - make it run and wriggle the cable a bit....

Or

An overheat cut-out operating to save the motor - it may be a real or an imaginary overheating (i.e. the cut-out switch may be defective) - the motor relies on a continual stream of driven air for cooling - if the air is restricted the cut-out saves the motor catching fire. Similarly if the brushes are badly chewed up then the motor will also run hot.

Good luck...

Peccavi
April 2013