Hard to do anything about this if you aren't providing any logs/examples of this happening. If you are having issues with the Plex TVH plugin, you need to seek support from the plugin developer, not us.
Just an FYI, I've never seen an issue with tvheadend leaving a channel stream open, possibly something to do with your hardware? My setup is a Digitbit R1 Network Tuner which is controlled by TVHeadend and the content is viewed via Kodi and it's TVHeadend PVR plugin.