I would suspect a bad bearing or possibly a bad chain as the reason for you having to change the gears out twice before. It's likely that the bearings are allowing the extra "play" and that is causing the slack in the chain.
Without having it right here to look at, it's really hard to say on that though. I don't know that your best bet wouldn't be to have a qualified technician take a look at the machine. Unless you can spot a bad bearing or something along those lines, I would really urge you to consider that.
I wish I could be of more help to you but with this kind of problem it's virtually impossible for me to direct you right to the problem.
You can go here:
Sears Home Services
to arrange for a technician to come see about your snow thrower.
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