It could be network issue / network card going to sleep / power save on the server PC
In the log file supplied - it shows network card going down at this time
Jan 17, 2016 15:57:03:707 [1608] DEBUG - Network change.
Jan 17, 2016 15:57:03:707 [1608] DEBUG - NetworkInterface: Notified of network changed (force=0)
Jan 17, 2016 15:57:03:802 [1608] DEBUG - Network interfaces:
Jan 17, 2016 15:57:03:802 [1608] DEBUG - * 1 {9166CE70-BA38-11E5-A705-806E6F6E6963} (127.0.0.1) (loopback: 1)
and then coming back to life at this time
Jan 17, 2016 15:59:42:579 [1608] DEBUG - Network change.
Jan 17, 2016 15:59:42:579 [1608] DEBUG - NetworkInterface: Notified of network changed (force=0)
Jan 17, 2016 15:59:42:585 [1608] DEBUG - Network interfaces:
Jan 17, 2016 15:59:42:585 [1608] DEBUG - * 1 {9166CE70-BA38-11E5-A705-806E6F6E6963} (127.0.0.1) (loopback: 1)
Jan 17, 2016 15:59:42:585 [1608] DEBUG - * 2 {01F351C7-2632-4149-9378-57A9630F1B63} (192.168.0.12) (loopback: 0)
Noticed by the XBOX One - the logging of course only works when the network connection is restored as it is logging to the server:
Jan 17, 2016 15:36:10:215 [7880] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:36:10:600 [3996] INFO - [Plex for Xbox One] Michael-Server is available at http://192.168.0.12:32400/
Jan 17, 2016 15:36:11:820 [7880] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:36:12:290 [3996] INFO - [Plex for Xbox One] Michael-Server is available at http://192.168.0.12:32400/
Jan 17, 2016 15:36:14:728 [3996] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:36:15:145 [7880] INFO - [Plex for Xbox One] Michael-Server is available at http://192.168.0.12:32400/
Jan 17, 2016 15:37:54:294 [3108] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:37:54:632 [3108] INFO - [Plex for Xbox One] Michael-Server is available at http://192.168.0.12:32400/
Jan 17, 2016 15:59:42:986 [4764] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 404)
Jan 17, 2016 15:59:43:418 [4764] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:43:766 [4764] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:44:120 [4764] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:44:421 [4764] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:44:737 [4764] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:45:070 [4764] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:45:292 [5236] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 404)
Jan 17, 2016 15:59:45:894 [1060] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:46:257 [5236] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:46:558 [5236] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:46:928 [1060] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:47:276 [1060] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 0)
Jan 17, 2016 15:59:47:429 [5236] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 404)
Jan 17, 2016 15:59:48:000 [1060] WARN - [Plex for Xbox One] Michael-Server is unavailable at http://192.168.0.12:32400/ (Status 404)
Jan 17, 2016 16:00:45:920 [0384] INFO - [Plex for Xbox One] Michael-Server is available at http://192.168.0.12:32400/