Are you logged into Skype / Messenger on any other devices?
This is a relatively new (very bad) behavior. I have a Skype phone system connecting to a PC application via USB, as well as using it on my laptop and iPad. In addition, my wife also sometimes uses it. We have SkypeIn and SkypeOut and use it as our main phone system. I also have another Skype phone system, this one has its own access point. They all need to use the same account and all need to work.
This morning I was not automatically signed into Skype when I turned on my computer. I signed in and my contacts list came up, a couple of seconds later Skype closed and went back to the sign in screen.
I am running Windows 7 ans there was a software update last night.