Cloud customers using multi-factor authentication were locked out of their accounts from 04.39 UTC on Monday US time (3.39pm Monday AEDT).
But issues around Office 365 appear to be still unresolved. On Tuesday, Microsoft was unsure of when things would be resolved to the extent that it posted a note saying the next update would only be at Tuesday midnight US time (11am AEDT Wednesday). That notice is still there.
As far as the cloud service itself goes, things appear to have been resolved late on Monday night, thanks to one of the ancient arts with which Windows are familiar. Reboot, reformat and reinstall were a standard remedy for borked Windows systems and used to be known as the triple-R salute.
"After attempting to fail over traffic to North America, this caused a secondary issue where servers became unhealthy and traffic was throttled to handle increased demand."
And regarding the mitigation, Microsoft said: "Engineers deployed a hotfix which eliminated the connection between Azure Identity Multi-Factor Authentication Service and a backend service. Secondly, engineers cycled impacted servers which allowed authentication requests to succeed."