You havnt said what type, but I am guessing it is a filter problem and the motor thermostat is kicking in....remove and clean the foam filter and screen on the side (if you have one) and allow to dry thoroughly. I also had a similar problem (cut out after about half an hour) which turned out to be the 'Lifetime Hepa Filter' underneath the waste drum (DC07, Animal). Removal is a bit tricky, prize out the clips with a flat bladed screwdriver. You can run the machine without this filter - get a replacement if this is the problem. In, addition check out all the tubes are clear and the brush is rotating freely.
Malcolm X, September 2007