My guess is that even if you can manage to repair it, you'll get more and more of the same issue happening.

If you have enough seal skin to recover it, that's probably the sensible thing to do. Getting the old cover off may be easy, but you may have to scrape some of it off, depending on how it was glued originally. That's good; it'll give you a rough surface to glue the new seal skin on.

At the saddle shop, they always use contact cement for permanently gluing leather and other skins together. Look at your local Tandy store. Don't buy the rubber cement; buy contact cement.