I agree with what the above poster said, in many games you have to reach a certain "save point" in order for progress to be saved. Which two games are you talking about? My son could probably answer the question with that info.
I doubt your son could answer the one..

it's a miley syrus game (or whatever her name is.. lol)
It did save a few minutes ago.
The other game is Dogz, the one you get free with the pink DS. Maybe she didn't go far enough.