Here is an article that alludes to the possibility of burnout in math competitions.
http://www.artofproblemsolving.com/Resources/articles.php?page=pc_competitions(I'm still skeptical of the story that the OP's son's friends, mother's friend's son dropped out before college due to math competition burnout, and not a combination of other reasons. But anyway, the story prompts an interesting discussion.)
Like many things, there's a question of balance. Even with high ability, effort/training/preparation/practice can be important for achievement/success. Too much exertion can lead to burnout, and at the same time no amount of exertion can make up for a too large difference in ability. (I mean, only an idiot would think that 10,000 hours of practice could make them a world class golfer if they weren't already at an extremely high level.) In a competitive activity, sometimes instead of trying to be the best, you should be happy with your best. And it's okay to quit activities that are no longer rewarding.
Activities like gymnastics, chess, ballet, sport, music, etc. should be the right combination of challenge and fun. But very few make a career out of these. Competing in math contests isn't a career either (though it can help one). But while someone at the 99.9th %ile (of math ability) isn't going to make it at the highest levels of math competitions, someone at the 80th or 90th %ile can have a rewarding career that makes use of their level of math ability. It's a question of perspective.
