Since today we encountering an endless authentification for the second Office 365 account in the profile on different computer running this Outlook version.
The login is successful the dialog closes and immediately opens again. When canceling the dialog the account is disconnected. Only solution so far was to remove the account from the Outlook profile and add it again.
I'm running an older build on this machine and everything works fine, but I'm curious - are those accounts both from the same O365 tenant or different ones? In general, you should open a support case and report this to have it properly investigated.