Had same problem with my dc07 , the root cyclone part kept blocking causing loss of suction and the motor would overheat causing it to shut down for 30 mins or so . I rang the dyson helpline , told them the problem and they sent out a new cyclone/bin assembly free of charge , this cured the problem for about 6 months but it now again has poor suction although it does not cut out now .
Dyson helpline 08705 275 104
Adam Parker
August 2005