If you have confirmed that it is not a case of the firewall blocking avast.setup, e.g. it gets past the firewall check but fails to update, read on.
There were problems, reported here about issues of automatic and manual update on the update to 4.6.731, a very large thread ensued. Are you getting the 0xC0000005 error?
http://forum.avast.com/index.php?topic=17501.105 and finally this statement
http://forum.avast.com/index.php?topic=17501.msg151378#msg151378.
The problem appeared to be due to anti-piracy checks at update reporting that the Pro registration key was invalid/keygen and effectively blocking the update.
Some of these keys may have come from people purporting to be resellers of avast! and until recent changed to the anti-piracy checks they got by. Now they are being picked up.
So if you bought your copy of avast Pro at the avast web site you should be able to contact them at sales @ avast.com with details of the problem (a link to this thread would help) where they can check your registration key/details and/or continue in this thread. If you bought it through a third party you should contact them and sales @ avast.com with details so they may chase it up.