not saving game data

i recently purchased a psp - problem is i can not save game progress - e.g. - gta - liberty street stories -
i reach a point in the game and nothing else is saved - i keep returning to same spot - i inserted a 2gb
dual memory stick(showing plenty of room left) please help with any ideas.

Might seem like a dumb question but the most logical might be the answer in this scenario so i'll ask anyway...

Are you going to the save icons in the game and accessing the save game menu?

Or does it not let you access it at the save icon?