Mine had the same exact problem. The lift quit working and I could not find a replacement part. It was some type of gear system and it was stripped. I was told I need to replace the whole mechanism.
The seat is bolted to the lift/slide mechanism, and mechanism is bolted to a pedestal which is bolted to the floor. The chair is quit heavy, so make sure you have a helper.
Let us know if you fixed it and how.
2006 Gulf Stream Tour Master T-36