I am posting this for Android TV but I can reproduce it on my tablet as well.
I have tested this same channel on the HDHomerun App and Emby and playback is fine on those even after 15-20 minutes of playback.
The channel is from HDHomerun's Premium TV service.
I submitted diagnostics from the Android Mobile app on my tablet as we are watching something else on the Shield TV.
Thanks for the logs. Looks like the connection is timing out because the HDHR stops sending video data for longer than we expect.
I am not sure if the issue you're seeing is server side, but I did just update the DVR software and went to watch the AMC channel again to see if the issue was fixed.
While it did take longer for the freeze up to happen, it's still doing it. Is the issue within the App or Server? I ask because I haven't seen an app update and maybe just need to wait for that?
EDIT: Oh, I and I did send another diagnostic log or whatever from the mobile app. Should be around the 8:56 pm time stamp.
The issue I saw was on the app side, but you could try with Tuner Sharing enabled to make it go through the DVR to see if that helps.