I have been fighting this same thing for a few days now. From what I can tell, everything works fine when the computer is first turned on - only after the computer has been running for several hours (sometimes idle) do I see this problem. It appears that Blink is denying all outgoing network traffic, regardless of Application Rules. I know this to be the fact because of the event logs - they show the TCP requests and the action as denied.
In my case, at least, Firefox would not connect to anything unless I enabled the "Allow outgoing TCP connections to port 80 / 443" system firewall rule. Same thing for Thunderbird - I had to create custom system rules to allow outgoing TCP traffic to the ports the email client is using. True, a reboot corrected the problem, but only for a few hours until the problem resurfaced. The other alternative is to turn off the firewall, which I am not ready to do.
The problem with enabling the "Allow outgoing TCP connections to port 80 / 443" system rule is that it seems to overide any application rules. Basically, with that system rule enabled I no longer receive prompts when an application is attempting to connect to the Internet. Reseting to default configuration did not help, in my case.
If you ask me, this is a problem with eEye's latest update. Hopefully they can fix it so that I can crank my settings back up to full strength.