Though this could seems an outdated post, I forgot its core so I will write it down again.
I would to share some advance Office 365 troubleshooting techniques I used to investigate problems with sign-in, activation, authentication, installation and update.
Troubleshooting Authentication/Sign-in/Activation Errors
To investigate about random user problem, usually sign-in prompt, you should enable Office 365 logging and compare a “working attempt” vs a “non working attempt” to compare the results.
Launch cmd as administrator and run the following command:
reg add HKCU\SOFTWARE\Microsoft\Office\15.0\Common\Debug /v TCOTrace /t REG_DWORD /d 1 /f
Once the error occurs collect the following logs:
Collect logs from %temp% Office.log <appname>.exe.log (where <appname> is the name of the application used for the Sign-In attempt, for example, Excel.exe.log or Winword.exe.log)
Remove the regkey added. To do this, launch cmd as administrator and run the following command:
reg delete HKCU\SOFTWARE\Microsoft\Office\15.0\Common\Debug /v TCOTrace /f
Note: if you are, as in my case, in a RDS environment, you should create a GPO to deploy/remove this registry key and cooperate with the users to collect logs when error popup