1. We have an article in the knowledgebase that has a link here... Outlook keeps asking me for my password or PIN. This is a bit technical but it is well documented and should be your first approach to try and fix the problem.
2. If you are logging into you laptop using a PIN number rather than your user name and password, please change to using your username and password. This is type of login has fewer issues than PIN login and may resolve the matter
3. If the issue persists... IGNORE IT. Move that login dialogue to off your screen or out of the way. Your e-mail will still flow in both inbound and outbound.
Microsoft sends out Windows/Office updates every month - sometimes more often. One of those fixes, which are applied automatically, will clear the issue in due course. My experience of this is that - as long as e-mail is flowing ignore the login dialog - annoying though it is. This may not sound like a very "scientific" solution, but Windows and Office 365 are very extensive and complex systems - that mostly work very well. This is the most time efficient fix for this problem.