I've had that issue in the past, and here's what I've gathered. This is not proven 100%, but may give you a slight edge to preventing it.
I've heard that the autosave fail is triggered by pressing "Y" (replay the level) too quickly after completing a level (touching Bandage Girl). It probably interrupts the auto-save that normally happens when you touch Bandage Girl, thus glitching it up. It's usually avoided by just watching some of the replay, just a second or two so the autosave is guaranteed done.
Generally, I've found that you can verify that autosave is working correctly in two ways. If the little "autosaving bandage girl" icon is appearing in the bottom-right when you beat a level, things are probably fine.
But if you want to be fully sure, go try playing a level with a bandage
you haven't gotten yet. Get the bandage and complete the level. If the bandage appears on the map screen on the level you just beat, things are fine. If it doesn't then the glitch has occured. Yeah, it sucks, but just exit back to the Xbox dashboard and re-launch Meat Boy and re-do what you missed.
As long as you're constantly aware of if you're autosaving and keeping the bandages, you should be fine and not miss too
much if the glitch occurs.
Hope this helps!