I'm having the same issue with Avast 2014's firewall on my Win7 64-bit machine. I use Ceton's ETH6 CableCard tuner, which lives on my network. Any number of 6 tuners can be assigned to any compatible Windows machine on the network.
This machine was behaving fine using 1 of those tuners, able to tune live TV over the network without any trouble. After updating from Avast 2013 to 2014, the firewall is blocking my network tuner and I'm no longer able to tune TV. I've added the required ports to the Avast firewall rules per Ceton installation instructions, but it doesn't seem to make any difference. Live TV will only tune properly in Windows Media Center if I re-add the tuner while Avast's firewall is disabled. As soon as the firewall portion is enabled, the tuner no longer works.
What has changed from 2013 to 2014 Avast versions' firewall that would make this an issue?? My main media PC (also Win7 64-bit) uses 4 of the tuners and has no issues with the recent Avast update because it is running Avast Basic 2014 and therefore does not use Avast's firewall. My only solution right now is to disable the Avast firewall (which I've paid for) and use the Windows Firewall until Avast can remedy the problem. I will not be renewing my paid subscription if this issue cannot be resolved.