It happened to me sometime that, I do not know why, my Outlook 2016 client start to ask me again and again my credentials of my firm account and at the beginning I did not understand why: in fact accessing the same email account from the email app, everything worked fine.
At the end I noticed that in the windows popup, the proposed username is not the firm correct one but is, by default, the email. If this is also your case, you have only to click the More choices link and change your username appropriately, taking into account to set also the domain in the username (yourCompanyName/yourCode)
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Check if the proposed username (by default your email) is the correct one: otherwise click on the More choice link