For a while now, my WDTV Live no longer shows up under ‘Shared’ in the Finder on my Mac. However, the WDTV can still access my Mac via the ‘Playback’ Media Server.
I don’t know exactly when this happened, but it happened somewhere between the lasted firmware update (1003.07) and updating my Mac from 10.11.4 to 10.11.5.
Thank you for you reply Summit48. I’m embarrassed to say that I have now solved the issue. The ethernet cable had popped out! So now everything works fine again.