I've recently starting seeing the above error with ever-increasing frequency on our build server. Nothing has changed in our TeamCity configuration during this period, so I'm guessing it might be changes at GitHub that are causing the error.
I've tried changing our VCS polling interval from 60s down to 600s in case GitHub was doing some kind of connection throttling, but there has been no affect.
Is it possible to make TeamCity less sensitive to connection timeouts?