Hi CarDonBo,
The licensing token for Microsoft 365 is valid for 30 days. Do you use Single sign-on?
If not, after user login into RDS, go to %localappdata%\Microsoft\Office\16.0\Licensing
folder, check the licensing token in the authString TXT file.
I also suggest you go to Credential Manager > Windows Credentials to remove credentials related to Microsoft 365.
Besides, go to Registry Editor, locate to Computer\HKEY_CURRENT_USER\Software\Microsoft\Office\16.0\Common\Identity\Identities
, and then delete Identities registry.
(Serious problems might occur if you modify the registry incorrectly. Before you modify it, back up the registry for restoration in case problems occur.
Please refer to this article about how to back up and restore the registry in Windows: https://support.microsoft.com/en-us/kb/322756)
Here are two similar threads you may have a look.
Office 365 User Login Prompts Continually Appear on Terminal Server
Office 365 on RDS keeps asking users to activate every logon