Ok, I found a solution here: [Link to 2k-forums][1], at least for my problem. 
Xcom seems to have problems handling to many save games. So, go into your save game folder (e.g.: "C:\Users\<Username>\Documents\my games\XCOM - Enemy Unknown\XComGame\SaveData") and delete or move old save games. Et Viola!



  [1]: http://forums.2kgames.com/showthread.php?154871-Save-game-bug-Sudden-loss-of-save-games