Go to Settings - > Apps and clear the cache (not data) for each game.
Do you have the most recent AB versions?
Also, doesn't AB connect to the Internet? Maybe you have a connection issue with their server.
Still a problem? Then email their support.
Lastly, do as the previous poster recommended (and what AB support will likely tell you) and uninstall/reinstall. Yes, I think you'll lose your progress, though I'm not positive. Try it with one game and see what happens. FYI, I don't have this problem with the two AB games I have after updating to 4.2.