May have to do with the 5.1 audio. When you record with surround sound there are 2 streams recorded, the Dolby 5.1 (6 channel e-ac-3) and stereo (2 channel aac). There may be a problem with Plex/Facebook and Dolby 5.1 given the licensing fees Dolby charges. I personally haven't had problems with Plex and AC-3 streams, but that's after I pass them through Handbrake when I rip blurays so it may clean up the file in a way that Plex can read.
I'd try a video with the surround sound disabled and see if that works. If it does, you can always strip out the 5.1 sound stream. Follow the directions
here, but make sure you only choose the 2nd stream when re-muxing. I played around with it this morning on my computer to see if it would work for another thread, and it seemed to remux properly with the h264 video and stereo audio
You can also just re-encode the video with Handbrake and choose the output audio stream type that you want.
EDIT: If you choose to re-mux with the Shana encoder mentioned in the article, you need to do this to get the audio to work properly:
Right Click File Name > Video/Audio Stream Selection > 0:2(und): Audio: AAC....
ADD
Then make sure you remove the 0:1 stream above the 0:2 you have added in the lower right hand box