I have now had this happen 4 separate times and once with my own account. I am a Cloud Partner and the other 3 were with client mailboxes, 2 of which were CEOs, so this has been a big problem for me.
While this problem does seem to go away after a time, it is now 4 times in the past month out of about 200 users we manage.
Problem is that Outlook suddenly loses connectivity for no apparent reason. Webmail and activesync continues to work fine and in the one case where the user had their Outlook configured on a second computer, it continued to work fine.
Also, during this time Outlook autoconfigure (for a new profile etc) stops working, but just for this user! All other accounts (and tried this from multiple machines) for the same domain configure just fine.
This "outage" has lasted from 2 hours to 3 days and needles to say is very disruptive to the users.
I spoke to Office365 support and they seem aware of the issue and their response is that "it should go away after a while." They don't seem to have a fix. Needless to say this is alarming and they need to get a handle on this.
The point of this post is to make sure others are having the same issue and to have them chime in and perhaps if there are enough of us they will figure out what is going on.