Managing personal Outlook.com account settings, security, and privacy
When I click to see any recent login activity, there is none listed. I've seen plenty of activity in the past.
Because Microsoft nerfed the Recent Activity page. It's now totally useless for routine monitoring. See:
About all you can do is check your Recent Activity page for a "Successful Login" that wasn't you. And by then it's too late, they are already in.