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.
This is more than ridiculous! I can see there about 670 people complaining about the same problem and Skype to my mind does nothing. How can Skype instill confidence to its users with no problem solving? We rely on this service which does not meet expectations. And some of us like myself pay subscriptions for our calls.. We cannot depend on your service if our PCs and iPads sign us out with no warning. And may I ask about Skype's silly question when one signs in "please keep me signed in". This is SO POOR. You better do something about it and reimburse us for our subscriptions.
Open your Skype account settings page:
If your Skype account is linked with Microsoft account, then try to unlink them.