Hey Angela, make sure to back up your Arkham City data if you’re playing it on the 360. The official forums of Batman: Arkham City has many posts relating to the save data being deleted without warning. A rather extensive thread on the subject reports heavy amounts data loss on all XBox models.
There is no real pattern to the save data, whether you’re a few hours into the game or you have completed it. According to one user on the forum, this issue existed in Arkham Asylum, and could be circumvented by quitting the game while on the dashboard. If it’s truly an engine problem then the same bugs will crop up.
This isn’t the only issue Arkham City has had, DLC problems were cropping up, and now save file issues that have been a moot point since we stopped using batteries to store data. A handful of users in the thread have outright said they will take the game back or no longer purchase any WB games if the issue is not fixed in surprisingly mature ways.
It could be people turning the game off while still on the save screen or something like that, I recall an issue similar to this happening several years back to a game I have since forgotten. If someone makes sure to be out of the save menu before turning the game off, and still has problems, let us know in the comments.
No patch has been released to my knowledge.