One possibility is that you have a firewall "protecting" you from the dangers of GitHub. By default, SSH uses Port 22 and HTTPS uses Port 403. I am not sure what utilities are included in cygwin, but you can test this by connecting to Port 22
$ ssh -T git@github.com
$ telnet github.com 22
and Port 403
$ wget https://...
$ curl https://...
$ telnet github.com 403
I tend to have the opposite problem: some of the servers I use allow outgoing connections on 403 but block 22.