I had the same problem with mine,
in fact it does not slide like the ones that I removed & re-backed with duck canvas. Another subject-sort of!
You have some good advice in the previous messages. There are two sections of doors on that face. If youdan, try to rock it back & forth and use silicone spray on the upper & lower track contact area, with the dirction tube inserted so you don't have it everywhere.
I had so many stick that I removed most of mine and broke the individual pieces out and re-backed them. GlenCoombe's advice on removing the piece is good. You may have a bent track gate, where the roll lides onto the track.
If it is hanging up that way do not force it. Get a couple of small pic tools. They look like minature awls (or ice picks). Make sure one is a 90' bend. You may be able to free the stuck area.
I may yet take mine out. Since next years project just became plumbing it will be a small project to fix the door! I agree that Tambour is not as bad as it is made out to be. Good luck.