At 1:30am Microsoft reported that issues with Office 365 related to mailbox connectivity have been resolved. Here is the official response:
Final Status: Engineers connected the affected users to replicated capacity to restore service availability.
User Experience: Affected users were unable to connect to the Exchange Online service. As a workaround, users may have been able to retry connecting as the issue was intermittent.
Customer Impact: Customers reported that they experienced this issue.
Incident Start Time: Tuesday, May 12, 2015, at 11:50 PM UTC
Incident End Time: Wednesday, May 13, 2015, at 8:30 AM UTC
Preliminary Root Cause: A portion of the Exchange Online service infrastructure became degraded.