Check the timings of the error messages in event viewer with sites that you visit that include the facebook connection logo, see my first screenshot above. Open Tweaking.com main page and you will see the facebook connection icon, then check event viewer for the DNS lookup failure error. As Facebook is banned in China, the great firewall is blocking the DNS lookup.
Your browser will be attempting to do a DNS lookup for these in the background (Prefetching), so that in the event you click on the icon it will speed up browsing, in the same way it will prefetch links as well. I have outlined the solution above.
In Firefox, set "network.dns.disablePrefetch" to "true".