I recently switched to Avast after being a Symnatecc/Norton customer for years and I’ve been using Avast for a few months now. I use the Plex media server on my PC to stream to my Playstation 4 and everything has been fine between Plex and Avast up until the last 24 hours. On Tuesday, January 31, 2017 Avast and Plex on the Playstation 4 were working fine together and then after work on Wednesday February 1, 2017 the Avast firewall is blocking the Plex server on my Playstation 4 for no discernible reason. I can confirm this is the Avast firewall that is causing the issue, when I disable the Avast firewall I can connect to the Plex server on the Playstation 4 just fine, if the Avast firewall is on it blocks the Plex server from connecting on the Playstation 4, simple as that. Avast firewall does not block Plex server on the computer hosting the Plex server. I didn’t change anything anywhere in the less than 24 hour period that this started happening. Tuesday night Plex and Avast firewall were getting along fine. I shut off everything and went to bed. Got up Wednesday morning, went to work. Came home started up the PC and the Playstation and suddenly Avast firewall is not blocking the Plex server on the Playstation 4 out of nowhere. I don’t know how to fix this because I don’t even know why it is happening all of a sudden.
Check the avast (firewall) log(s) to see what is blocked and set the appropriate rule for it in the firewall.
The logs for the Firewall show no blocked traffic since after this post. I got a new router and it is working fine. My old router had glitched and set IP addresses on my network to different than the originals. This was not the problem though. New router with new IP addresses and Avast Firewall is still blocking Plex. The Firewall specific logs show no blocked addresses/ports since February 2nd. Yet on the summary window for the Firewall that shows Most Recent Blocked programs it shows the firewall blocking both Plex Media Server and Plex Media Server DLNA Service. Both of these programs are set to allow all connections in the Application Rules for the firewall.
I’m facing the same problem. Plex worked perfect prior to the Avast update. I was able to access my plex media server remotely. But now, Avast keep blocking Plex Media Server as well as Plex Media Server DLNA Service and Hosts Process for Windows Service. Please Help.
Are you using Private or Public mode on the Firewall?
Ironically, I toggled with the Private and Public mode on Avast Firewall like an hour. Did it just now and set it to Private and things are perfect again. Don’t know what i did the past hour but thanks! 
Could you show a screenshot of your Avast Firewall and the Avast Application settings of the Plex Server?
How does one switch between private and public firewall setting? I don’t know how to do this and have not messed with it since I have no idea how to do it.
→ https://www.avast.com/faq.php?article=AVKB25 (Firewall FAQ)
I saw nothing in that faq about switching between public and private setting.
This resolved itself…sorta. I had not applied the lastest update to Avast that added the new screens where there is the public/private setting for the firewall. It was set to public and once I set it to private it started allowing Plex again.