I've come to the conclusion that this is/was a Steam problem, so I appologize for posting it here on the games forum. I do appreciate the responses though. I did a complete uninstall and reinstall of Fallen Enchantress, and started playing my first game. I'm happy to say that I just got back from exiting the game with no issues.
I think it may have had something to do with the way Steam updated the last patch, because I did briefly enter and exit the game when I first bought it, before I had the time to play it, and I had no problems back then.