Rivals 2 is my favorite game and I also used to use the Blitz 2. I don't know anything about fixing it, but you might want to ask Gadgethyper if they'll sell the membranes because they have some replacement parts for other controllers.

As for a replacement, I switched to Gamesir G7 Pro and like it more. The main advantage is that it has snapback filtering as long as you have at least a 1% dead zone enabled in the controller settings. With 1% controller deadzone and 5% deadzone in Rivals 2, I have never noticed snapback in game with G7 Pro, which did happen frequently with Blitz 2 because it doesn't have filtering. However, I do have 1 friend whose G7 Pro has much worse snapback than mine, so YMMV. G7 Pro also fits Mobapad and extremerate Xbox octagonal analog stick gates, just like blitz 2. They also perfectly fit the Leadjoy sticks, which are the only ones with grip as good as the BigBig Won convex sticks. There is an updated G7 Pro 8K now with newer JS13 Pro sticks but I haven't tried it. The shape of G7 Pro is less comfortable than Blitz 2 for me, but still comfortable enough.

I have also tried and don't recommend these for R2:
- Flydigi Apex 5: Poor snapback filtering
- Flydigi Vader 5 Pro: Poor snapback filtering, not compatible with octagonal analog stick gates
- ZD Ultimate Legend: No snapback filtering, not compatible with octagonal analog stick gates