Signle Sign On and Outlook

First of all, can you clarify what exactly you mean by Single Sign On, as the term can be loosely used to reference different things. Is this a federated scenario, or are you using the AAD Connect "seamless SSO" feature or? Also, did you check the user UPN, any form of SSO will only work with custom domains, not the default onmicrosoft.com domain. As a best practice, make sure that the UPN and the primary SMTP address match.

You should also consider opening a support case, as these forums are not really intended to be a support channel and we can only give some basic suggestions without having access to additional data.