I agree- the 3rd child to have such issues? Warning bells, especially as it did get as far as quitting for the other two.
Elite is a whole different animal. You never see your child, they push themselves to their limits, often get tired, and emotional. It's difficult to see what's "just" the sport taking a toll, and what's true unhappiness. You commit as a parent too, make sure they don't miss training, worry about progress, if it's all worth it...
You will ask yourself a million times why are you doing it. Sometimes you hate it, sometimes the child seems to hate it. But there is something freaky about such kids. For mine, it's just what she does. If she stopped there would be a huge thing missing from her life, she's not that kid that likes to watch tv or read. She'd be coaching herself on the sofa.
We had a slight issue with her coach in the summer. I couldn't see it, but she was saying he was being mean and she couldn't please him. I suspected it might be a language/culture thing, but having grown up in the 80's, I am also very sensitive to bullying styles of coaching.
What we did.
Explained to DD that while x might be one of the best coaches, he was no good for her if she wasn't happy. She wouldn't reach what she was capable of, and might even quit. We also talked about the culture difference, different coaching styles, frustration, and when he said x, y, and z, it didn't mean he thought she was rubbish and might as well quit, it meant she could do better, and he wanted her to focus. Also reassured her that as long as *she* was happy, we were happy for her to go elite, step back and do it for fun, or even quit, now or ant any point.
Said we could speak to the coach and ask him, reassure her he still was happy with her.
Explained that there were things we could do. We could ask for her to step back a little and have a different coach. She's young and 6 months off elite track, heck even a couple of years with the "right" coach, wouldn't harm her eventual career. We could ask to cut a day, even two, and maybe look at something complementary like ballet or acro/rhythmic for a while. None of this needed to be permanent, she could step back up (or not) any time she wanted.
We could change club. Always an option.
We put a time limit on it when she didn't want us to do any of that. Said if she felt the same at the end of the summer (so 2 months), or she was still having teary fits/seemed less than happy, we would discuss it again.
She did have a few more episodes, but after the summer things chilled out a bit, big comps over, back to training rather than preparing for comps. Then a two week break over christmas, and this morning she got up and said she couldn't wait for training tonight. I think it was culture clash, general tiredness, competition stress etc. I'll still keep a close eye (and I also have her teachers school watching for any behaviour changes).