The model ID starting in 944 indicates your tiller was manufactured by Husqvarna. This division has since been purchased by AYP. A quick online search finds that www.needlawnmowerparts.com
lists having one for $55 plus shipping. I have not dealt with this company, so I can't recommend or not recommend them.
It is very common for tiller makers to not offer internal transmission parts. Transmissions are difficult at best to repair and reassemble. Used tillers are available from time to time, check your local classified ads or www.craigslist.com
to find one. If you decide to go with a new tiller, i would recommend trying www.northerntools.com
to start your search.
As far as longevity on the new transmission, Sears won't guarantee any of their parts longer than 1 year. However, you should expect a replacement part to last as long as the first one did.
Sears doesn't give year models for their equipment, but usually supports replacement parts for at least 10 years. Most equipment manufacturers don't build their units to last longer than 10 years....they want you to buy another one.
I hopethis has helped.