Two things come to mind.
First, Ironman heros will never save in modern Windows. This has something to do with anti cheating methods they used. It's said that the game needs access to the registry but Windows won't allow it so it can't save the hero. I think the mod The Protectors fixed this issue but otherwise as far as I know there's no help for it.
Second, for non ironman heros the game normally saves on the system partition (typically c:) so again Windows might prevent it from accessing the directory it needs. If that is the issue first make sure you're running the game as administrator. If that doesn't work then make sure the game isn't installed in the program files directory as Windows sometimes won't allow programs to access it.
I haven't had this problem persist otherwise so hopefully that solves it.