It hasn't happened to me in the middle of a movie, but it just happened to me when I tried to go to My Computer on the aTV a couple weeks ago. I tried restarting this and that, signing in and out of Homesharing on the aTV, turning Homesharing on and off at the computer, rebooted, restored to factory... all to no benefit.
It ended up being that my iTunes had signed out of the iTunes Store, for some reason. Signed back into the store and everything worked fine, again.