I faced a problem with skype that it logs me out automatically just after login. After R&D I got solution. So I want to share with you all.
Actually this issue nothign related to any malware or your machine issues, just log into your account on skype.com. and check if your account is linked to micrsoft or not its linked than unnlink it by unchecking the box inf front of microsoft account link. and the quite frome the application and login again you will never phase this issue again.
Hope This may help you!