I think I found the fix so I put it up here in case anyone else runs into this issue.
I think it relates to secure connections and certificates. This link is slightly related but i found it as my LG TV started to exhibit the same behavior i initially reported but it was all the time (and not just after a few hours of the server being on)
Since i made this change my PS4 and LG TV have had no issue connecting to the server at any time. Its been probably a week and approx 5 situations where i have used plex from either device so id like to say i am reasonably confident.
Settings -> Network -> Secure connections is set to Preferred. (I already had this set)
So i think this setting fixed it - Settings -> Advanced -> Allow Insecure Connections is set to Always
I dont use plex remotely so the risk is low for me setup.
Hope this helps
