Unlike most features of Visual Studio, the Git tools do not (always) automatically pick up the Widows proxy settings, being dependent on a number of open source libraries which don't seem to be benefiting from the same Windows Proxy Auto-Detection.
This is a shame, really, but it doesn't make it impossible to have Git for Visual Studio to pick up a proxy server.
To configure your proxy server, you must set an Environment Variable called "HTTP_PROXY". It follows the same configuration scheme as Team Explorer Everywhere. After setting the variable, restart Visual Studio if you had it open when changing the environment.
Most cross-platform applications will try to use this variable, if applications suddenly start to behave strangely, they might be under the influence of this variable. In my case I picked up such behavior in Calibre Ebook Management.