To disable network connections in Post Affiliate Pro edit accounts/settings.php and add following line there:
Where the issue comes from? Well, this is more likely a Curl issue, so it means, that you may have some kind of firewall or some server configuration that does not allow Curl connection to the servers of qualityunit.com.
Here is another example of the screen. I also added screenshot of the Firebug message:
If you can find an animated image on the right of the POST requests, than check it and try to find Gpf_Install_CheckVersion or something similar... If it is there, than this is surely the network problem...