From Windows Live Help:
Error 80072efd: You cannot sign in to Windows Live Messenger
You may not be able to sign in because of problems with your firewall (A security feature designed to help protect a computer from unauthorized external access. It can be hardware, software, or both.) or proxy settings. Visit another website to confirm that you're connected to the Internet. If you are connected, check your firewall settings and adjust your proxy settings:
Check your firewall settings
1.Go to the MSN Web Messenger website.
2.Click Start MSN Web Messenger, and then try to sign in.
If you can sign in to MSN Web Messenger, but Windows Live Messenger still can't access the Internet, Windows Live Messenger may be blocked by a firewall. You may need to add MSNmsgr.exe to your firewall's allow list. For more information, see your firewall's documentation or website.
Adjust your Windows Internet Explorer proxy settings
1.Open Windows Internet Explorer.
2.On the Tools menu, click Internet Options.
3.On the Connections tab, click LAN Settings.
4.Clear the Automatically detect settings check box.
5.Click OK, and then click OK again.
Note
For more information about the network ports and web addresses that Messenger uses, see
Network ports and URLs that are required for Windows Live Messenger 2009 to work.