Windows 8 dislikes more than one instance of an application.
If you try to start several instances of any program from the start screen, be it Paint or Remote Desktop Connection, it will fail. It takes you to the instance which is currently running. After all, why would you start more than one Remote Desktop session or perhaps have more than one Paint open at the same time?
Apparently, Microsoft thinks they have a better idea how many instances you are allowed will need to have open. Which is, well, only one.
The "solution" is to go to Desktop, right click on the icon of the running application in the Taskbar and start a new instance from there. This "solution" is of course, completely invisible and illogical to the regular user.
Yet another reason that the start screen is foolishly designed.