Do you play on Steam or the TTG installed version?
If TTG, can you please check your Documents\Telltale Games folder to see if you have a Gamedata folder and a Walking Dead folder? If so, your save games are probably being stored in one folder and your game content in the other. The Walking Dead folder is the standard directory for both, so please remove the Gamedata folder from your computer.
Alternatively, if you have Steam, check your Steam directory in steamapps\common\the walking dead to see if you have a prefs.prop file here. If so, please delete that file.
Now restart your game and see if you are able to save your progress. If not, you may need to uninstall the game and remove all traces of it from your system and the reinstall.