If you’re running into strange Plex issues with your HDHomeRun tuner, you’ll need to upgrade to a modern HDHR product to fully resolve them. Plex officially supports HDHR’s entire product lineup since the beginning of time, but in my experience it just doesn’t play well with older devices.
For years I was never able to reliably tune Live TV on Plex Web 100% of the time. (See my closed thread about it here: Live TV viewing works about 10% of the time) Streaming devices worked great, but Plex Web always gave me trouble. Tuning channels would result in either a flawless stream or timeout errors.
That thread indicates that I fixed the problem, but it came back after the thread was closed. 
Out of desperation I moved my PMS installation from Windows to Ubuntu on all-new hardware. That changed absolutely nothing - the problem was still there even on a fresh install on a different OS!
Today I replaced my HDHomeRun Dual (HDHR3-US) with a HDHomeRun Flex 4k (HDFX-4K) and the problem is completely gone.
To be fair, my tuner was old. The HDHR3-US was released in 2011. It still worked great, just not with Plex. So if you’re seeing weird tuner issues and your HDHR is a few years old, think about biting the bullet and buying a new one to replace it.
I can’t tell you how long I’ve dealt with this issue and how many different config changes I’ve tried through the years. I basically had given up on having live TV through Plex in a browser at all. Now I’m good. $200 poorer, but I’m good. 
