It is a problem, particularly if the school are not aware of it or refuse to recognise it.
Dd1 found so many things easy at school, that she assumed it was her birthright to be able to do any task immediately, perfectly, and better than anyone else. She was completely unable to cope with situations where the answer was not immediately obvious to her, or where her performance was not as good as others', and simply did not know how to persevere, or keep working away at a problem in order to reach the answer.
For her it was exacerbated by the fact that the school didn't see that there was an issue. She was consistently given work that was far too easy for her, and given cheery little 'excellent' stickers when she had clearly just scribbled down the first thing that came into her head.
It does get better, but slowly. For dd1 the key was doing activities that didn't come naturally to her -- it took her ages to learn to swim, for example, while the children who had started with her were promoted to two or three groups higher. I spent a lot, really a lot of time talking her through this, with conversations like:
Dd1: "Everybody's better than me at swimming."
Frogs: "No, some people find it easier than others, but you'll all get there in the end if you keep trying."
Dd1: "Well you're better than me."
Frogs: "Yes, well, I'm 27 years older than you."
Dd1: "Well God is better than me."
Frogs:
This was a real conversation, btw.
I'm not naturally one for making children do activities that they're not keen on, but in this context it's worth finding one or two things that they can keep plugging away at. Gradually she realised that it was okay not to be best at everything, and it was okay to be reasonably good at something but not perfect. She did Grade 1 flute and got a merit (how pleased was I that she didn't get distinction!), and was happy with that. She's now in Y7 in a selective but not massively hothousey school, where they are all expected to work hard and the staff are completely wise to people coasting. She has put in a lot of effort, and seems to be doing well in her end-of-year exams, but is chilled about the fact that some of her friends have beaten her in some subjects. Both my older dc have just joined a running club -- I know dd1 still has to swallow hard to cope with the fact that her younger brother is clearly better than she is, but she's taking it on the chin and is happy to keep going on the basis that it's good for her to get fitter and enjoy the activity even if she's not naturally gifted at it.
Keep plugging away. It is a slow process, but as long as you're aware of the issue in terms of making decisions about schooling and extra activities, it does slowly improve.