Well the update servers have been working fine for me.
What version of avast are you using, the latest is 6.0.1091 ?
What is your firewall ?
Does it allow avast.setup internet access ?
- If it does delete the entry for it and reconnect to the internet, this should force the firewall to ask permission again.
Do you use a proxy to connect to the internet ?
If not - Try this also if the above doesn't make a difference - From the avastUI, Settings, Updates, Proxy Settings, set it to Direct connection (no proxy), see image.