Check the filters. If they're clogged up then the motor will overheat and cut out. But your problem seems to be the common broken cable. Either the live or neutral wire breaks where it enters the vacuums' body.
UNPLUG THE MACHINE FROM THE MAINS.
Take off the dust box, and remove the top section. Just keep lifting upwards it will clip off its pivots. You'll see a torx screw holding a little panel. Remove that panel to reveal the cable and switch.
Remove another torx screw clamping the cable.
Press and release the on/off button.
The on/off switch should pull out now. Pull off the cable terminal, then slacken the screw in the terminal block and remove the neutral wire. Pull the cable out of the machine.
Holding the cable in one hand and very firmly pulling on the live and neutral wires individually in turn should reveal the broken conductor.
steveD, April 2008