The belt on my Dyson DC01 keeps breaking. At the point where the belt is breaks (it only breaks across about 50{e5d1b7155a01ef1f3b9c9968eaba33524ee81600d00d4be2b4d93ac2e58cec2d} of the width and then comes off) there is a lot of wear as if it has jammed and spun on the motor shaft. There are signs of wear on the plastic casing parts as if the belt has been rubbing. In fact some of the thin plastic webs next to the path of the belt are cut through.
The agitator brush has a raised, bevelled section on which the belt runs. Through use, this has a tendency to wear. This can cause the belt to drift across and cause the problems you describe.
In this scenario, a new agitator is required. Best contact Dyson, as there were variants as to the type of ends employed.