Fine you want logic? Here you go.
This is from Ho-oh's black and white pokedex entry: "It is said that those who see Ho-Oh are promised an eternal happiness."
Ash saw Ho-oh on the first day of his journey and multiple times since. There are two key words above, eternal and happiness. What makes Ash happy? His pokemon journey, or his quest to become a pokemon master, and all the fun things that happen along the way. This happiness will last forever, or be eternal. This is why Ash has been on a pokemon journey for such a long time and does not age. He finds happiness in his journey, and his journey will be eternal (i.e. he will not age).
This is the only logical answer I can think of, other than the real one "he's a cartoon character". Just my two cents, and this is not my original idea.