I'd recommend you read
this post from Saturday. Parts of it will sound familiar.
If she still loves the sport, gym, etc.. I personally wouldn't make her quit over a mental block. I'd look for a mental coach and try to get her team coach and mental coach talking if needed and they are willing. If money or resources are an issue or if you have concerns for her long term health or safety, of course, you are the parent and should do what you think is best. "My kid might hold it against me" is never a good reason to make a decision for a child. Everyone dislikes SOME decision their parent made. We all have to grow up and *hopefully* understand that - assuming we had loving, responsible parents - our parents did what they thought was best. If they have kids, they'll do the same when they grow up. The coach said that she would tell you if it gets to a point that she needs to retire, I'd trust that. But this really is just part of the sport. They all struggle with something - some more than others. Mental blocks, reoccurring injuries, etc..
Editing to Add: This is all assuming that she's in a good gym environment. If she's not in a good, supportive environment, you need to look at moving her to a different gym. Mental Blocks can not improve unless she believes she is safe and supported.
From what I've read and observed, she's at that peak age timeframe when the kids start to get more nervous. I've observed that they eventually hit a point where either they don't want to deal with it anymore and are done, or they find a way to work around it. Either way, they resolve the problem themselves. The parents/coaches just help them see the options, which you've done. Quitting ends the problem.. but it's not empowering if it's not their choice. If it's at all possible, I'd try to be patient. Mental Blocks take time. Lots of time. I'd recommend that this is a good time for you to step back, stay out of the gym, don't talk about it except to give her a hug and show her you love her, support her, and believe in her *as a person apart from also in her gymnastics*.. and let your girl, her mental coach, and her team coach do what they can do. It's
hard to do that as a parent, but from my observations across 7 years and 2 gyms.. that really is the best thing you can do. And I promise you, I've BTDT. Everything you've discussed plus back-to-back injuries. More pressure on her won't help move the process along. Yes, it's hard to continue to pay what gymnastics costs when things are rough.. but nothing worth doing is easy. And the $$ probably wouldn't cross your mind if she was just continuing to work on a skill, not having a hard time on something she "should" have...
Perhaps think of it that way. For her, this is like getting that dreaded kip. This one is going to take a while. You just have to have faith and be patient. It'll be whatever it will be. But she wants it, so you got that going for you/her.
Here's my go-to "It'll be ok" Gymnastics Song, just for you guys.
And send me a message if you ever need to vent or talk. It really helps to have someone to talk to when you feel you've already said it all a million times, but it's still there.
Good luck out there <3