I know a way to use both Skype and Messaging.
First of all, you should config Skype not to run in background. While Skype is closed, Messaging might not display this error. You can open Skype and use it normaly. After using Skype, close it, and if Messaging still displaying the "Not connected" status,
close all the Messaging, People, Calendar and Mail apps, go to Desktop Task Manager, and finish the Communication Services task. Open the Messaging app (it automaticly restart Communication Services), and the status might be online, or off-line, the way you
want.
I think, every app or site that changes you online status (like Hotmail page, or skype), affect the Messaging bug.