I had that same problem a while back. Besides worn diff nut it can also be a broken outdrive itself! The diff outdrive(joint?) is like a cup, the bottom of this cup takes a lot of force. In my case, the bottom rim of this "cup" had a small split/crack in it so there wasn't enough resultant clamping force on the diff plates, hence loose diff.
Maybe my english is bad but I hope you get what I'm trying to say?..