I've got an old Cub Cadet 2165 tractor with a 40" snow attachment (190-303-100) and when I installed it last week I inspected the belts and they looked fine. Then, we got 6"-7" of snow. A few minutes into using it, I briefly smelled a burning belt. It went away and I kept on going. Ten minutes later, the auger belt failed.
By the grace of god, I was able to find a 1/2" x 79" belt at Autozone. I installed it and went back to work. I finished the driveway, but once in a while I smelled a hot belt. I kept checking it and it was very warm.
To me, it seems like there's extra friction from something causing it to slip. Without the belt on, I was able to spin the auger pulley by hand without much difficulty so I'm kinda confused.
First thing to check are your pulleys, especially the idler pulleys. If they are not rolling straight and smooth you may have found your problem. Second is the belt routed properly and not overly tight.