I would recommend rebooting your router and modem/etc as well as your PC, and try the update again -- make sure that your Internet connectivity is OK
If that doesn't help, try an Online Repair of Avast (Control Panel -> Add/Remove Programs -> Highlight Avast -> Click Change then select Repair)
If you continue to have issues, can you check your DNS settings? Some users who have had trouble have reported that changing to Google DNS resolved the issues (perhaps your DNS is blocking the servers for some reason)