Same problem here. AVG fails to connect to the AVG servers to download updates. Following the suggestion of the failure message that appears on screen, I checked the connection settings. Everything is set to their defaults, and it is not trying to do anything funky like use a custom proxy server or anything like that. I've also checked firewall settings (on this PC in particular, it is using the default Windows Firewall, which doesn't not make any difference when it is turned off).
So, uninstall and reinstall? Will that do the trick? Or is there something else that I can try?