I've been playing offline and haven't had a completely corrupted save, but I did have one issue that made me have to restart.
I was starting the Mad Hatter case and was fighting the goons at the beginning. It appeared to be a good room for the particular Shadow Vigilante challenge I was on, so I restarted after missing what I was going after. When the game reloaded from the restart option, I was falling continuously. Restarted again and the same thing happened, so I quit to the main menu. When I chose my safe file, it showed the file I was on and everything looked fine. Showed my percentage and difficulty correctly. However, when I clicked Story Mode, the Continue Story option was no longer available and it was replaced by the New Game button. It seemed to know I had a game in progress because when I pressed New Game, it asked me if I was sure I wanted to overwrite my current game, but I had no option anywhere to load that particular game back up.
Even weirder, when I started the game over, I had all my Riddler packs still collected, all my upgrades, etc. I even had the story related gadgets straight from the get go, well before they'd normally be obtained. The only things that had gone away were my progress in the main story and the cases that I had done and the progress in the Dark Knight challenges. Still annoyed to have to restart, but at least I don't have to re-collect the Enigma packs that I had found so far.