First thing I'd try is pulling down the notification bar to view all notifications and then tap on any hdmi entry; it might just disappear.
Could be related; If I switch to another video source on my monitor it can kill the hdmi connection to my phone, requiring an unplug then replug.
Not sure about the data com specs in hdmi, but there may be signal modes communicated by the monitor like: turn off hdmi (like what happens to me when I switch sources), turn on/off hdmi depending on video activity, or set hdmi to an always on state ( like whats happening to you ).
Different equipment combos will likely have very different results, I'm guessing.