This happens to me sometimes...
It happens when you have bad batteries.
How to check if your batteries are bad:
Open the battery case and turn the battery around.
If your Game Boy restarts, then your batteries are bad.
Read the GBA instruction booklet to see what kind of batteries are the best.
I've had a game (Pokemon Crystal of all games x_x) that just turned the screen white after a few minutes on my GBA. So, try a different game. If this is with all games, try what the other poster said.
If you're too scared to open up the battery cover, how is it that you have fresh batteries?