Make sure Avast has the correct permissions in your firewall.
Also provide us more information.
How do you connect?
What are the settings for updates in Avast?
What OS?
etc etc.
Try delaying the update on boot.
C:\Program Files\Alwil Software\Avast4\Data\avast4.ini
Open this file in Notepad and browse for the section in brackets [InetWD] you must add a line like this:
You appear to be missing avast.setup this file requires access to the internet to perform the update.
This is not a permanent file like the others but created at the time of update. Try a manual update and ZA should ask if it can connect. If ZA doesn’t ask check to see if ZA hasn’t blocked it.
Somthing is preventing Avast to connect to the update server when you boot the system.
You can use StarrUp Delayer (link in somewhere on this board) to arrange the things that are loaded at boottime. Give it a try. It solved the problem for a lot of people already.