I am also having this exact problem with my Haswell Win 8.1 setup. The second I turn off my upstream HDMI receiver (Onkyo TX-NR905) the Intel Display Audio device will disappear from the "Sound, video and game controllers" section, and I will get an exclamation mark on the "High Definition Audio Controller" under "System devices". And from there the only option is to reboot the system to get the audio back. Picture is working as expected.
Hardware: Asrock Z87E-ITX (bios 2.10) + i5-4570T
Tested every driver combination avilable from both intel and Asrock (including audio driver 3129), and they all fail the same way. I have even tried using combinations of various audio drivers from different driver packages (as suggested as a solution in another thread) with the same result.