When attempting to resolve mail server errors/issues, being able to test the connection to a remote SMTP server is a critical step.
Testing a remote SMTP / mail server connection should be done from both a local machine (computer) and the server experiencing the issue.
From your terminal (shell) window perform the following:
dig MX hotmail.com +short 5 mx2.hotmail.com. 5 mx3.hotmail.com. 5 mx4.hotmail.com. 5 mx1.hotmail.com.
telnet mx1.hotmail.com 25
Trying 220.127.116.11... Connected to mx1.hotmail.com. Escape character is '^]'. 220 BAY004-MC4F30.hotmail.com Sending unsolicited commercial or bulk e-mail to Microsoft's computer network is prohibited. Other restrictions are found at http://privacy.microsoft.com/en-us/anti-spam.mspx. Sun, 1 Feb 2015 08:27:01 -0800
Trying 18.104.22.168... telnet: Unable to connect to remote host: Connection refused
It's not my preferred method, however you can always try external services for SMTP server diagnostics.