"The Steam authentication servers are not responding."

This means your client was unable to get the necessary details from Steam required to login to the server.

Usually it happens when your PC has temporarily lost connection to Steam. Especially on Tuesdays when Valve performs Steam's weekly maintenance. Unfortunately there is nothing you can do about it except try again later. It might be a one-off issue, or it might persist for a couple hours. If it has been happening for a long time (say, 8+ hours) there might be a problem with your network preventing a connection to Steam.

Ordinarily while online Steam will cache these details so it should be a relatively rare problem.

Behind the scenes

This means ISteamUser::GetAuthSessionTicket failed / returned an empty buffer.