We recently switched our users over to Office 365 from an on-premise Exchange 2010 server. For the most part everything is humming along like clockwork. However, a few users are being asked by Outlook to enter their password. Through my Googling I found many people talking about constant password re-prompts which isn't what's happening here. As long as the user enters the correct password, Outlook connects and email flows normally, they're then not asked for their password until Outlook has been closed and reopened.
We had a slightly different issue recently where Outlook couldn't complete the autodiscover process when setting up new profiles and it was determined by Microsoft that a simple registry edit would tell Outlook to stop trying to talk to our old server. Thinking that maybe the same was happening here I implemented this...