Today, Windows agent-side checkout from GitHub stopped working at 11 AM PST. This must be related to the deprecation of TLS pre-1.2 at that time.
Agent-side checkout uses some sort of JetBrains custom SSH client, apparently to receive the GIT SSH key configured for the VCS root. This now fails to connect to GitHub.
I'm assuming that this is because we're still using 2017.1.4, and the latest version can still perform agent-side checkouts from GitHub.
Workaround that worked for me: Set "teamcity.git.use.native.ssh=true" on all agents' buildAgent.properties, copy passphrase-free ~/.ssh/config/id_rsa on to all agents for which GitHub has the public key.