something could be blocking access to the avast servers. you could try disabling your HOSTS file by renaming it to "nohosts," and see if that resolves the problem.
usually, the HOSTS file is located at "c:\windows\system32\drivers\etc."
if you use the "spybot s&d" antimalware-program, my guess is that it generated a HOSTS file that is causing the problem.
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As it's only one of the two servers (speed and security) that Pro accesses in Health Check then it could well be an issue at that one server,
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If it's at the server end then nothing <em>you</em> can do will change that.
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Give it a few hours and try again, if it still won't connect then it could be your antivirus or firewall that is blocking that particular connection.
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In that case it sounds like it's being blocked at your end - I would check your AV, firewalls, hosts file etc. to see what may be blocking the connection.