You didn't mention what belt it was, but the issues that cause a belt to come off are pretty generic and will apply anywhere.
Is it the right size?
Are all the belt guides in place?
Is the tension right?
Is the alignment correct between the pullies?
Many times with the old Sears tractors, the belt guides around the pullies are either removed or bent. This is usually caused by many belt replacements over the years.
Where is the belt coming off? The engine, the transmission, etc.... If you can narrow that down, then take the model number of your machine and look it up on the Sears Parts site to make sure the belt guards and guides are on your machine. Some of the guides are nothing more than roundstock bent in such a way as to keep the belt from slipping out of the groove when power is disengaged. These guide are usually easy to rig up or make in the shop if need be.