I can confirm the latest Avast interferes with my Usenet downloads as well. I had been downloading without incident up until late evening yesterday, then at some point Avast auto-updated (though it didn't restart my PC), and suddenly all Usenet downloads just stopped. Restarting my downloader (NZBGet), rebooting the computer, nothing helped.
Then I remembered I'd been using secure downloading with SSL, and my downloader was configured to use a SSL cipher called "RC4-MD5". So in NZBGet I removed the RC4-MD5 selection (which would let the SSL library auto-negotiate a compatible cipher with the server) and restarted it, and my downloads suddenly resumed.
Now, I didn't know that Avast could be to blame until I found this thread. With Avast Mail Shield set to scan NNTP, I re-enabled RC4-MD5 in NZBGet and restarted, and downloads hung. Then I disabled NNTP scans in Avast, restarted my NZBGet again, and it's working once more.
So clearly something in the Avast update is interfering with NNTP, specifically the RC4-MD5 cipher in SSL.