I have an iMac 2013 and have been having this issue from 10.8 - 10.10, basically same as everyone HDMI output to my LG tv works only after restart and goes away after the mac sleeps, not sleeping it is not an option. Finally I gave up and thought that maybe the hdmi cable was the issue, or the TV was not compatible etc. Then I decided to play around with an Ubuntu live usb, and that thing slept, woke up and everything was still fine, switch the tv to cable and other inputs and went back to the mac and everything still worked.
So now something tells me this isn't hardware! Decided to try bootcamp and install Windows 8.1, everything worked perfect for a couple of days, then my wife switched the input to watch live tv, and then the AMD High Definition audio playback device disappeared from the list of playback options (hdmi video works fine). Couldn't get back the audio device even after rebooting and going back to OSX (the hdmi output worked though), so I tried removing the device from the device manager and refreshing again. And it is working again, somehow the device stopped working and only after reinstalling it back does it start to work, I've tried it several times now and 100% the device would come back and hdmi audio output would resume.
My question now is how do you remove and reinstall a device in OSX to mimic what I've tested on windows 8.1? Right now I'm just happy how well it is working and that I'm able to use xbmc and the pc at the same time.