The Problem
I've really loved XBMC on the NUC I acquired several months back (see here). Until just a few weeks ago, it had been hooked up directly to my television via HDMI. I had not had a single problem with it until that point, which was when I purchased a receiver and connected the NUC up to the TV through it. There was no sound, although the video still came through to my television fine. Nothing that could be changed in XBMC's audio options made a bit of difference.
The Solution
After a bit of searching on the OpenELEC and XBMC forums I came across an odd solution. Changing XBMC to output in 720p instead of 1080p made the sound work. This thread on the OpenELEC forums made it seem like it was an issue with all of the 3.2.x builds of OpenELEC. Not satisfied with the 720p solution, and not wanting to have to downgrade to an early version of XBMC, I decided it was worth trying a nightly build of OpenELEC. It worked, and now I have 1080p and working digital audio to my receiver. It does mean that I have to use Gotham, the next version of XBMC, but thus far stability has not been a problem.