The second link points to a registry key that simply does not exist for me and is seemingly not applicable in Outlook 2016. Links I've tried will be at the bottom of this post. I've seen a few other folks with this problem, but those fixes don't work for me.
I've removed his password info from Credential Manager. I don't know if it matters, but our O365 setup uses ADFS. I've reached out to the mail team, but I've been told there's no changes that have been made that should cause this. I run O365 personally and I'm able to get it to have me enter a password each time, but our organizational one won't. I'll update the post when I get that information. As far as I know, it's Windows 10, but I'm not sure of the Office version. I'm working on getting details on the system it's working on. This seems to work on one of his computers, but not the other. I have a client here that wants to be prompted for his password every time he opens Outlook.