How did Henry Mills grow up in a town where time stops and no one ages?

It's not the town that is cursed, it's the residents, but only the residents that were in the fairytale land at the time the curse was cast.
They are only being contained in Storybrook. Stroybrook itself is not cursed, so uncursed people can easily pass through with complete ease.
Henry was an uncursed person somehow brought to Storybrook door Mr. Gold.

this is just a guess.
i think that if your from the fairytale world u dont age.
but i dont think Henry was born in storybrooke but raised there door Regina.
Idrk:)

The last person who answered is absolutely correct. The other people are not ageing because of the curse that Regina cast while they were in fairytale land. Henry was not born until many years later, and he was born in our world, so the curse does not affect him.