Thanks for the logs.
Now for the not-so-good news.
You’re having a lot of internet connectivity issues. PMS gets a connection (getPublicIP), find Plex.tv, then loses it a few seconds later.
Aug 22, 2017 11:27:18.492 [0x7f30373ff700] DEBUG - PublicAddressManager: Got public IP from http://plex.tv: X.XXX.XX.XX
Aug 22, 2017 11:27:18.646 [0x7f3020fff700] DEBUG - HTTP 200 response from PUT https://plex.tv/devices/f398a11ba649598dc95482beb5a3e837e3790ee1?Connection[][uri]=http://192.168.1.11:32400&httpsEnabled=1&httpsRequired=0&X-Plex-Token=xxxxxxxxxxxxxxxxxxxx
Aug 22, 2017 11:27:26.096 [0x7f3039ffe700] DEBUG - handleStreamRead code 335544539: short read
Aug 22, 2017 11:27:26.137 [0x7f303a7ff700] DEBUG - Auth: We found auth token (xxxxxxxxxxxxxxxxxxxx), enabling token-based authentication.
Aug 22, 2017 11:27:26.137 [0x7f303a7ff700] DEBUG - Auth: authenticated user 1 as asagarra
Aug 22, 2017 11:27:26.137 [0x7f303a7ff700] DEBUG - Auth: Came in with a super-token, authorization succeeded.
Aug 22, 2017 11:27:26.137 [0x7f300a7f5700] DEBUG - Request: [192.168.1.36:54716 (Subnet)] GET /player/proxy/poll?deviceClass=pc&protocolVersion=1&protocolCapabilities=timeline%2Cplayback%2Cnavigation%2Cmirror%2Cplayqueues&timeout=1 (5 live) TLS GZIP Signed-in Token (asagarra)
Aug 22, 2017 11:27:26.138 [0x7f300a7f5700] DEBUG - Beginning read from two-way stream.
Aug 22, 2017 11:27:33.387 [0x7f3039ffe700] DEBUG - EventSource: Connecting to 109.237.24.233
Aug 22, 2017 11:27:33.387 [0x7f3039ffe700] DEBUG - EventSource: Resolved to 109.237.24.233
Aug 22, 2017 11:27:33.497 [0x7f303a7ff700] DEBUG - EventSource: Connected in 74 ms.
Aug 22, 2017 11:27:33.497 [0x7f303a7ff700] DEBUG - EventSource: Wrote data, reading reply.
Aug 22, 2017 11:27:33.595 [0x7f3039ffe700] DEBUG - EventSource: Read HTTP reply header.
Aug 22, 2017 11:27:33.595 [0x7f3039ffe700] DEBUG - MyPlex: We appear to have regained Internet connectivity.
Almost immediately, it loses it and resets
Aug 22, 2017 11:29:34.962 [0x7f3039ffe700] DEBUG - PublicAddressManager: Obtaining public address and mapping port.
Aug 22, 2017 11:29:34.962 [0x7f3009ff4700] DEBUG - PublicAddressManager: Obtaining public IP.
Aug 22, 2017 11:29:34.962 [0x7f3039ffe700] DEBUG - EventSource: Failure in IdleTimeout (0 - Success).
Aug 22, 2017 11:29:34.962 [0x7f3039ffe700] DEBUG - MyPlex: We appear to have lost Internet connectivity, resetting device URL cache.
Aug 22, 2017 11:29:34.962 [0x7f3009ff4700] DEBUG - HTTP requesting GET http://plex.tv/pms/:/ip
Aug 22, 2017 11:29:34.962 [0x7f3039ffe700] ERROR - EventSource: Retrying in 15 seconds.
This cycle continues throughout your logs.
I can only suggest a steady ping test and/or iperf test to track down why you’re losing connection / packets. The last I saw this there was a damaged / worn ethernet cable. If you’re using Wifi then your server is not getting the minimum connectivity needed.