I can't add an O365 email to Outlook desktop client but I can access it from the web

Hi there- I am an non-IT person looking for help on this topic. I have an O365 license for my LLC and access my email through the desktop version of Outlook. I work with another business as a 1099 contractor that requires me to have an email under their domain to use when dealing with their clients. This email is accessible through Outlook on their O365 license. Up until a few months ago, I was accessing this email by adding it as another account to my O365 Outlook desktop version. Then all of a sudden it stopped working. I can still access the online version. 

I've tried fixing through their vendors, but all troubleshooting to this point has not resolved the issue. They were suggesting that the other company provide me with another Pro license, which was really not a solution. It appears that I need to troubleshoot through other means.

Checking here to see if someone would be able to help. I have added/deleted, restarted, logged in/out of accounts more times than I can tell you. I've tried checking the "prompt when opening" button in Control Panel, as suggested here. Nothing works. Below is a screenshot of the error message I'm getting. 

I get this even though I have not been prompted to enter User ID/Password or when I do. Once in a while I get past this and it adds the account for a few hours, then it stops working. 

Any help or guidance would be appreciated. Again, I'm not an IT person - just a freelance business consultant. 

Thank you in advance for your consideration!