Had a similar issue on my older Simplity Regent. Turned out to be a couple things, but not the pulley or belt. First, the bolts holding the axle/transmission assembly in place had loosened, which subsequently put less tension of the belt and misalignment of the belt on the pulley, so re-tightened them. Thread locker on those bolts would probably help as well to avoid the issue in the future. Second, some of the blades on the fan itself had moved upwards slightly, probably due to them being plastic and aged. Only discovered this after doing a slo-motion video when the transmission belt was engaged. It was those blades that would touch the belt just enough to push it off the pulley. In the short term, I rigged up a band between the pulley and the fan blades that, in essence, was a pulley guard to prevent the blades from touching the belt. Seems to have done the trick and saves pulling the tranny off the tractor, at least for now.
Yes definitely worth checking the fan. Glad you fixed your problem. I had missing bolts and a broken bracket that supports the transmission before this issue. It’s a good idea to check all the nuts and bolts once a year. The front bracket that supports the deck occasionally needs tightening.
Most of us can not do what you did. I need a simple solution to belt coming off the transmission pulley .To replace a worn belt the steering shaft has to come out. WHAT A DUMB DECISION BY SIMPLICITY'S ENGINEERS & DESIGNERS. We need a belt that can be threaded through the pulleys then re-attached to itself by a clip, staple or whatever it takes to replace the belt. There has to be a better and easier solution.