OK - I had this issue with iTune movies downloaded from store, newly with iTunes 11.1, affecting all movies, even those that were once fine. The sound plays fine (Apple cinema display & sound) in large window mode but disappears on fullscreen (repeatably, coming back if fullscreen is exited).
A fix that works for me is to switch back and forth between playing on this (my) machine and another local authorised machine using Airplay - of course you can do this without interrupting playback and without exiting fullscreen using the button on the control bar. On re-selecting 'computer' after allowing the switch to complete the sound comes though fine, and this seems more-or-less stable once done*. I do not know if the other machine works, too (it is a server with no normally-on display).
FTR things that do NOT work include permnissions repair, reboot, re-alunch iTunes etc.
*PS - it works but is not stable; you can switch in and out of fullscreen without losing sound but if you switch movies (or come back to a movie previously watched) you have to go round the loop again. We need 11.2 please Apple!