@jdavis83 Sorry - I know that this thread is a few years old.
I have a fairly similar setup and configuration to you - including down-time freakily. I recently moved from windows to OS X after using a MacBook Pro for work, and like you, it’s working great inside my home network, but mine is temperamental serving remotely (sometimes find it’s not available). I’ve tried the usual tricks - UPnP off, no double NAT (that I can find) and manually set the port. When it loses remote access a restart of the server seems to cure it.
What version of Plex are you running? (I’m on the latest version 1.4.3.3433). I had similar remote serve issue with windows and found that using an older version I had in my downloads ran smoothly it (so installed and didn’t update) - but don’t have access to an older Mac version of Plex 
cheers
