Since the buy over, the Microsoft team has been trying to integrate Skype into the Microsoft ecosystem.
One very annoying recent change has been to lock the windows taskbar if you have an unread message or notification. While this might seem to be a useful change, it also negates all the screen burn benefits of screen savers i.e. the taskbar is displayed 24×7 until you have read and discarded the notification.
Luckily, Skype allows you to remove its icon from the taskbar when you close the Skype window (Skype still runs in the background allowing you to receive messages etc).
Now all you have to remember to do is to close our Skype window.