The save system sucks, big time. Using the 360's Dashboard to handle everything, you are torn away from the game when you save. Guide Blades swoop in from the left and right, it is all very confusing. Surely they could have covered together a better system. Oh, and you only have one save slot.
When you die (and you will die) you have two options. Save progress and restart the entire game, or load last save. I just started day two and encountered my first auto save.
This is a game you are very likely to play again, so there is no need to force people into only one save file.
Beyond the rotten save system, the game is a hell of a lot of fun.
UPDATE: After playing the game for a few days now, I like the save system now that I understand it. It adds to the intensity and urgency of what you need to do.