Mayor Gravity
I've always wondered this, and want to know other people's opnions.
I've read teh J,M Barrie book, but I don't remember it ever actually disclosing it.
If you're looking for a literal, physical reason in the book, you're not going to find it. But if you pay attention to the themes and subtext, you'll see it: in the book, the aging process is essentially a natural side effect of maturing and progressing as a person. However, Peter refuses to progress and grow as a person - because that would mean accepting pain and responsibility - and as a result remains forever frozen in time. The book makes it clear that this is a bittersweet situation, because while he is functionally immortal he ends up forgetting everyone he ever knew. Furthermore, the only form of love he can feel is that of a child toward a mother, which is a selfish rather than selfless form of love.
Adults can also refuse to move on in this world, too. While Captain Hook's age is never explicitly made known, it's revealed that he was contemporary with Barbecue, or Long John Smith. This would mean that Hook was alive in the middle of the 18th century, whereas the book is set in the early 20th century. Hook's own miseries and demons are linked to his refusal to move on emotionally - he is obsessed with getting vengeance on Peter, and he lives in constant fear of the crocodile. He only escapes his misery when he gives up on his revenge and embraces the final change - death - by jumping into the jaws of the crocodile.