My daughter had problems with shutting down and crying especially if she got something wrong or failed at something.
When she was 8, I enrolled her in a local kung fu afterschool program (combo child care/martial arts class). The master taught them pride in themselves via real achievement and didn't take any crap (where to be fair, this behavior falls in the continuum of human behavior). He'd push her - if she started a form, messed up, started crying, he'd push her to start again and not just let her retreat into herself.
By the end of the year, she had a lot more confidence and failing at something didn't cause her to immediately get discouraged and abandon it and cry and stuff. I didn't tell the master about any of this up front, but he came and talked to me and he immediately identified her personal Achilles heel ("She's a good kid, the one problem she has is...") and gave me regular reports on her improvements on that front.
So basically, she needed her ass kicked a bit (call it "tough love" to sound sensitive) to get through it. And sometimes it's hard for us as parents to do that, even though we should, and this proved a good solution for us.