After updating last week, I am having this problem as well. With no connection to Xbox Live, I get stuck in a sign in loop. I start the game, it asks me to sign in to my profile, which I do. It then says that the "console can't connect to xbox live", do I want to exit and test the connection? After selecting "no", it states that I either have to sign in, or continue without saving. Choosing "sign in" again leads down this same frustrating path. Selecting "continue without saving" makes me watch your God-awful introduction/tutorial which some genius decided I can't skip through.
Thinking about it now, though, after doing this probably 50 times, I don't know which I'm angrier about: that it won't accept the fact that I'm signed in, or the fact that I can't skip a 5 minute-long tutorial. Honestly, who does that?
The suggestion of the user EarliestIowa8 worked for me (sign in loop): Go to settings, go to kinect, then go to the bottom kinect id settings. Allow it to rescan your face and move forward and sideways as instructed. The problem appears to be perhaps that either more than one player is using the same profile or it has not properly recognised your profile so it may pay to have all players kinect ID profiles rescanned. This seems to have worked for me and I can now play some of the games I was having problems with offline using the offline profiles. Good luck to all.