Plex DVR, Trying to watch Live TV but get error "Unable to tune channel (no parts)"

I have been looking at your logs which show that you have 2 devices with 4 tuners.

HDHomeRun 10339178 (192.168.33.110) - tuners 0 and 1
HDHomeRun 10381F37 (192.168.33.129) - tuners 0 and 1

The logs do show an issue that is being corrected for the next release of Plex Media Server - it is a problem where after a failure, subsequent attempts to tune get failed with a Plex Tuner Service logged error of no tuners available

This happened for example sometime after starting a 70 minute recording of WGN Weekend News at Nine - Episode 12-29 at 20:55 on 29th. Just over 60 minutes into the recording, there was a transcoder failure. The tuner was not closed down after this error and all subsequent attempts to tune on this DVR (10381F37) were failing with this underlying error No available tuners found to start streaming channel

For the other DVR (DVR 10339178), the logs show repeated failures to tune transponders for tuner 1 between December 27th 21:55 and December 28th 22:29. A couple of tunes for this tuner on the 2nd January were successful.
eg

Dec 28, 2018 22:28:29.678 [3096] WARN - [E] transponder_streamer::start_channel. Tuning stransponder for channel triplet://0:1003:1 failed

Dec 28, 2018 22:29:30.706 [2732] WARN - [E] transponder_streamer::start_channel. Tuning stransponder for channel triplet://0:1003:1 failed

This i would suspect would be a tuner issue.

The fix for the problem of not closing down the tuner after an error should be fixed in the preview release available here Much faster (hopefully), smaller (mostly) and better PMS builds preview (1.15.0.573-123756e9a) (Note that this is pre beta) - the fix will be in the next beta / public releases