The Plex Media Server process deadlocked sometime after Dec 27, 2018 14:55
You were running version v1.13.9.5456 at the time
There was a subsequent fix for one cause deadlocks in 1.14.0.5468
I would like to see if you still get these deadlocks after updating to the current version
After a deadlock and when the server reaches a backlog of over 1000 requests, all requests get failed with error response 503 as what happened here