I'm making this post in case it helps anyone else. I've got a Mac Mini (Late 2012) 2.3GHz i7 with El Capitan OS.
I had random pausing issues on all client platforms for several years, but most notably on Roku. The movies would start to play perfectly then after a random amount of time would pause and not recover. Sometimes stopping & restarting would help, other times not. This seemed to happen more when I was playing films outside the house than when I was home. Changing streaming settings did not help. Re-encoding my films did not help.
I would see error like this in my Plex Media Server.log file:
Feb 19, 2016 21:05:26 [0x70000073b000] ERROR - Error writing media: 32 - Broken pipe
Feb 19, 2016 21:08:52 [0x70000073b000] ERROR - CERT: Error in TLS handshake: short read
I thought I had obscure network issues (and perhaps I do).
Nothing I'd tried fixed the pausing issues.
Then I noticed that my RAM (4GB) was showing 'pressure' (but was showing about 3.7 of 4GB in use). I tried playing a film on the web client on the Mini, and it paused. I quit Chrome (a memory pig) memory use dropped to 3.3GB, and it played smoothly.
I replaced the 4GB with 16GB from Crucial (about $80). Everything is now working perfectly. Five movies played through with zero pause or re-caching. My system now shows about 6.6 of 16GB used.
To sum up: 4GB may not be sufficient if you're doing anything else with your Mini other than Plex.
Lesson: Check your RAM.
I hope this helps someone.