Let her quit?

There is nothing wrong with letting her quit. As long as she has fought to do it. Quitting when things get a little tuff is bad. But it sounds like you and you daughter have put up a good fight. Would it not be a good thing to show her to know when to stop? Give you and her a break. Let it go. There will be many other fights.

Good grief, give yourself and your daughter a break. Gymnastics thankfully isn't the only activity she can participate in. Just sit her down and ask her if she is really enjoying gymnastics. If she's reluctant to say that she really loves it, then tell her she can try anything else and you'll completely support her no matter what she chooses, if she chooses anything. She may be sticking with it simply because she doesn't want to let you down and feel like she's a failure in your eyes. In other words, maybe both of you want her to quit but your sticking with it for each other's feelings.

Don't feel like a failure as a mother for a start. I think your a brill mum. You wouldn't be on this seeking help otherwise. you'd give up yourself.
My boyfriend is blind in one eye, he can do hand stands and walk on his hands etc. So just because she's blind in one eye. doesn't mean to say that she can't do it!
Tell her not to give up! My niece does gymnastics. It took time and practice. Even in the garden at home she practices and practices. Now she can do them.. she's 9. She's been doing it sinse she was about 5. It takes time, practice and patience.
Tell your daughter, from me, that nothing is impossible. If she wants to do this, don't give up! Because it's something she's going to regret. Tell her to give herself the chance. Other kids may be better, she might suck at it. But fair play for trying. And if other kids can learn, she can too. and be just as good!
She probably can't do it because she doesn't believe in herself enough. You need to believe in her, teach her to believe in herself. Tell her not to give up on her hopes and dreams.
might take time. but she'll get there. without a doubt! I believe in her anyway!

Help her find something else that she might enjoy. Being good at something isn't everything...its more important if she enjoys it.

Yes, let her quit. Tell her that she should do things she enjoys regardless if she is good at them or not. Is it her depth perception that is causing the trouble? It's not your fault or her fault. You can't be good at everything. There is something to be said about knowing when to cut your losses. Anybody can play a hand. The secret is knowing when to fold.

Tell her she doesn't have to do it if she doesn't want to because there is no reason for her to have to suffer when she is supposed to be having fun! Oh, and by the way, she is probably afraid to fall, a fear that will keep her from doing any of the ridiculous stunts that they try to make her do.

I would encourage her not to give up at gymnastics. However, if it becomes something that starts to damage her self-esteem ("All of the other kids are better than me at gymnastics, so I must be really stupid and untalented" etc), than it's probably going to do more harm than good. If that happens, don't let it go too far-- you could allow her to try something else instead that she seems to show a knack for.

And my goodness! You're not a failure at all! I can already tell, just by reading the details of this question that you are a good mother. Especially the fact that you want her to become involved with these things and you want her to get life lessons out of them. That says a lot about how caring you are. If gymnastics doesn't work out, it's alright. These things happen sometimes, but it doesn't have anything to do with your role as a mother or her's as a daughter.

never give up and never back down shes your mom she needs you one day she will thank you

You are hardly a failure as a mother! If she wants to quit just because it is hard, remind her of other things she has accomplished that were hard. Things like swimming, singing and dancing in public, even limbing stairs can be tough for someone who is blind in one eye. If she quitting cause you are protecting her, maybe you should rethink that.

allow her to think about what SHE really wants to do. My daughter asked to join Karate. I was surprised and wondered if this would really be good for her. I let her do it thinking she'd lose interest after awhile. But it would be HER choice. She is now a world wide champion. Has won 5 gold medals in the junior olympics, has a 5th dan master degree and has excelled beyond my expectations.
Never underestimate what she can do. Simply allow her to be the one to choose what she wants to do.