Same problem, but it started following the installation of the latest QB upgrade. Using Office365 and for 2 years I have been sending out Invoices and Purchase Orders etc. without the need to enter a password, and now I get prompted to enter a password. Spent hours on a call with Quickbooks Support basically doing what is on this thread + re-upgrading QuickBooks, upgrading Office365 etc.

It seems that the problem is when you try checking the  "Use enhanced security" box the default server for Outlook/Hotmail/Live is 'smtp.live.com' but it should be 'smtp.office365.com'. (Using Office365  throws off email error messages until you make the server change in Preferences. However, when you check the "security" box you can no longer get any Office365 email to pass the webmail authorization process and you end up getting an XML error message in a QB Webmail Authorization box.

Support has no idea