Yeah, Majora's Mask has a bit of a wonky save system--there are two ways to save the game. You have to either play the Song of Time and return to the start of the Three Day cycle, or save at an Owl Statue, which interrupts the game and can only be loaded once. Dungeons are best completed in once sitting if at all possible (that's true of all Zelda games, of course.)

Actually, in Twilight Princess there is a way around this. If you need to save and quit in a dungeon, you can warp out using the Ooccoo and save outside, then return to the very room you left.