This has being going on for such a long time, and yes I have changed the HDMI cable.
The incoming aerial signal is split between an HDHomeRun Connect and a (Freeview) Panasonic DVR.
The HDHomerun is linked to Plex and I never have a problem recording TV (unless I have internet connectivity issue, because the Plex server is upstairs).
I record the TVNZ 1 News on Plex, but have issues with watching the news whilst it is still recording (it's my own fault in not understanding what I am doing wrong when trying to watch a Plex program whilst it is still recording).
The Panasonic DVR, whether it is showing Live TV or recorded TV, does not like TVNZ 1.
It doesn't seem to have a problem with TVNZ 6 or say TVNZ 2, Three or Prime (10).
I could easily wait until Plex has finished recording the TVNZ 1 News, but for some in my family, it is not an option (yes I know I could try TVNZ On Demand).
I can wiggle all the relevant cables and sometimes the pixellation goes way but most often does not.
The next time the TV is re-started, it can be perfect.
The one significant unknown is that the TV is on a TV cabinet with wheels, so we move the TV when we want to watch in the Kitchen or watch in the Family room (rotating the cabinet in the same room).
My post today is because tonight was bad watching TVNZ 1 (as was last night). Three was perfect tonight.