Variety of different issues to raise here; which (all) may be related to a similar issue. To try and cut out the extraneous background data; I first started using PlexMediaServer with a PS3 as a DLNA client. As my media collection grew; the limitations of the PS3's UI grew a little more than annoying; so I moved into using the Plex App on the PS4... Which is when things started to get a little weird.
When streaming to the PS3 over DLNA I never had an issue with playback when my ISP cut-out. When I moved to the Plex PS4 App I started loosing playback... whenever the internet dropped out. Which... odd? I've kind of just tolerated the drop-outs; swapping back to the internal Playstation DLNA media players whenever my ISP just decided to stop working overnight.
More recently though I tried the Plex App on a wireless connection Windows 10 tablet; and ran into an issue where despite being on the same network as the server... the Plex app kept telling me the Server wasn't available. I was only able to get to the server on the Plex App by telling the server to only prefer secure connections; and telling the app to accept insecure connections on the same network.
That behavior is also demonstrating itself on my wired desktop:
Both the Win10 store app and the Plex Media Player insist that I have an indirect connection... and give me pop-ups telling me to get more information about Plex Relay... when my desktop is on 192.168.11.103; and my server is on 192.168.11.142
Huh?
That um..
What?
I've gone over the Plex Server Settings; made sure GDM was enabled and that the DLNA server was turned on. As far as I can tell everything seems to be configured for the Plex apps to make a direct connection to the server; but they just... well... can't. I'm also now wondering if this Indirect Connection through the Plex App is also why the PS4 Plex App keeps cutting out everytime the ISP lives down to their reputation....