I don't think that he didn't get older at all. If you watch one of the first episodes and then one of the newest, there is a difference - in how old he looks, how tall he is and in his character. The new VA helps, too.
The show doesn't give too many hints on time. My guess would be:
Ash was 10 when he left Pallet and 11 when he fought in the Indigo League. That's what we know from the TV show. Then he traveled through the Orange Islands and Johto. Somewhen in Johto there was an anniversary of the day Ash and Pikachu became friends (=Ash's birthday). However, It's not said, if it is the second or third or whatever (Pikachu short of movie 3). I assume it could be the third as traveling the Orange Islands for sure took some time. So Ash could have been 13 years old when he fought in the Johto League. 14 would be possible, too. Then traveling through Hoen could have taken another year and the trip to the battle zone another 6 months. So Ash could be about 16 when he makes a new start in Sinnoh.
What I really do not believe is that the timeline in the anime is the same as our real time. The anime may be 10 years old but I don't think that in the anime 10 years have passed. In Japan they have 1 episode each week (if I'm not mistaken) and normally one episode takes place at one day. Sometimes even 2 or 3 episodes take place on the same day. Although there is much traveling between the episodes, I don't think it takes that long - not enough for 10 years to pass.