If there is nothing in your firewall log it is probably not being blocked. I had this problem in the past and a search of the Avira forum showed that the Norton removal tool had removed a Windows file that was used for the update. Maybe you have something similar?
I was able to download and replace the missing file which solved the problem.
I think the problem is with Avira itself. There have been long term problems with the updater since v9 which have been compounded in v10 and if you visit the Avira forum or Google it you will find that the general concensus is that Avira are not putting so much effort into the free version anymore due to its success as the best free AV which started to affect the sales of their paid one. I was a long time user of Avira free version (4yrs)but recently have installed MSE after having problems with Comodo AV, Avast v5 and the latest version of AVG. I find that Comodo Firewall on the proactive setting and MSE are very compatable on my PC and will continue using it for the foreseeable future as by far most of the reviews of MSE are positive.
Welcome to the poorest kingdom of Avira updates scheme… [/stop sarcasm…]
Indeed, I gave up on having Avira as a second opinion in my computer due to the annoying popups and the update scheme (slow servers, reduced number of servers, poor configurability…).
Right now, there are tests showing exactly this… They left the protection of the free version behind and are pushing only the paid one.