Checkpoints are always lost when you quit a level and you have to start from the beginning of the stage.But why I didn't start from the last checkpoint when I quit and then choose Highschool again? I'm assuming that's because when I quit I "unequip" the goth costume that I was using? So I have to somehow select it again and then start the stage? (Otherwise the game won't 'recognize' it?)
I heard you can resume checkpoints by shutting the game down via dashboard/XMB but never tried this by myself. To be safe I just played each stage without quitting