I have this problem too.
Previous setup which worked: Mac Mini 2010, OSX El Capitan, all the latest software updates applied. HDMI into Denon AVR receiver, which has HDMI into Pioneer 60" Plasma TV. No problem connecting via Screen Sharing then disconnecting - never lost picture.
What I changed: I completely wiped (with Disk Utility) the machine and reinstalled El Capitan completely, to try to resolve an unrelated audio issue** (see bottom for description, I didn't want to muddy the waters by mentioning it in this paragraph). Applied all OSX updates then installed Plex Media Server and Plex Home Theater.
Actions to cause problem: After Plex Media Server had finished syncing with my media library, I loaded PHT, ran through some on-screen settings via VNC, then disconnected the VNC session from my Macbook Pro, and the TV screen went blank as soon as my VNC session was disconnected.
Expected behaviour: Plex Home Theater should stay on-screen.
Workaround: reboot Mac Mini, disconnect VNC session immediately, i.e. before machine restarts. Log in using USB keyboard. If you have PMS and PHT set to load on login then you will be good to go. I just tried reconnecting via VNC again then disconnecting, and the picture does NOT disappear. So for now, I can't reproduce this problem, after rebooting.
My guess as to what causes the issue: Some people use Mac Minis as 'headless' (i.e. no monitor/display attached) machines or servers, and Apple knows this. So my thinking is that there's a bug where it thinks it's headless, and when you disconnect via VNC it tries to start the screensaver or something like that. I have worked remotely with Macs before administering them via VNC and I've had this issue - Airplaying video from iMac A to a room full of people, then disconnecting my VNC session (from my Macbook Pro to Mac A), and the room full of people say their video stops playing. Walk physically to iMac A and there's a screensaver or lock-screen showing (can't remember which, sorry - it was a few months ago in a very busy job). Could be worth playing with the screensaver & security settings to see if that helps. My security "require password 5 minutes after screensaver starts" setting is disabled,
**Unrelated audio issue was: Plex Home Theater would start to play back video incredibly slowly (1-2fps then eventually grind to a complete halt), the OS X sound preferences pane would refuse to load (usually giving an error message but sometimes just going into "Not responding" state and requiring a Force Quit), and if I crashed out of Plex Home Theater and tried to reload it, it would never finish loading, and basically only a reboot would fix it. That's just my "unrelated" issue (mentioning it in case it's actually a symptom for you guys too - otherwise, ignore what I've written here!)
