This problem is/was happening pretty often. There is no user side fix. It requires a support ticket. The details follow. The error message is:
Login failed. Despite our best efforts, something unexpected has gone wrong. Please check status.secondlifegrid.net to see if there is a known problem with the service. If you continue to experience problems please check your network and firewall setup.
This error started appearing about last Tuesday, 12/19.
It is account specific. You will be able to login with a different avatar from the same computer and viewer. Because it is account specific file a trouble ticket using the problem account at https://support.secondlife.com/create-case/. Alexa Linden also says contact Second Life Support.
If you have the problem and would like to help get it resolved, collect your logs immediately after you see the error and close the viewer. File those with a bug report in the SL Jira. Try BUG-11032 or BUG-11127.
This bug was supposedly fixed 1/4/16. As of 1/6 it is still happening.