Hi George,
It isn't just 8.1 ... it started with the move to 8.0. Essentially, you cannot start a second session from a desktop icon.
What you CAN do is start a second session from the File menu. So, choose File > Open from the menu, select your ATSP or ATLP file, and that will start a new session in a new Window.
You can also right-click on the tab of your current session, and choose Clone if you want a session to the same server - although this will open as a new tab in the same window.
Note that you can "tear off" a tab from a window to create a new window - so even if you start with multiple tabs in a window, you can create multiple windows from this.
Hope that helps.
Brian