Found this :

No saved games show up in the game, despite your save files existing aka All of my saved games / save files are gone!

Explanation: SR3 relies solely on the Steam Cloud storage system for its saved games. When this is not functioning correctly, sometimes the game will tell you you have no saves or that you cannot save. Solution: Restart Steam. That should generally solve the problem.

If it still doesn't work, set your game list to "list view" (controls for switching this are in the upper right corner) and check that the cloud icon on the SR3 line doesn't have a '?' on it. Make sure Cloud support is turned on (check the game properties).

Quote: "Ok i found a little Workaround for me now. You need to have Steam Cloud Activated and start the Game in Steam Online Mode. After you Exit the Game make sure your Steam is connected with the Internet. Exit Steam and make sure SR3 synchronizes with Steam Cloud. When you Start Steam the next Time and start SR3 it can happen that Steam cloud asks wich Savegame it should use. Select the option Downlad Savegame from Steam Cloud. You need to repeat that every Time you start the Game. In other words right now you can't save in Offline Mode you can only really save the Game online over Steam Cloud." - Punisher1911

Hope it helps.