We suspect this issue started to arise after curl was updated within the Plex Media Server software. The issue has been seen to arise when there are massive movies libraries scans. Libraries with more than 4100 movies have been seen to give rise to this - exhausting the dynamic tcp ports pool and ending up with tcp error event id 4227 logged in the windows system event log and after that tcp requests start to fail - eg the transcoder.
We are working on getting curl changed but I have no information on that.
If you do have a massive movies library, you could try out the new movies scanner which is on a forum preview release as from today - that changes how movies are scanned and we may use up less ports. See New Plex Media Server movie scanner and agent preview