I keep my Skype minimized in the Service Tray at all times, BUT it frequently opens itself up for some self-advertising purpose when I log on --- very, very annoying and I don't think it can be stopped. Over the years, Skype --- which originally was a great, multi-functioned, troublefree, free service --- has progressively become more annoying, more intrusive, and more expensive!
In regard to your actually disconnect problem, I can only suggest that you go to Skype help + support for some hopeful resolution. I know that there are several levels of help --- I'd go through all of them to see if you can get some personal response. Keep clicking on the "Get More Help" links until you finally get to the screen where they allow you to send them an email with your specific problem. (They don't seem to provide telephone tech support.)
My other suggestion would be to go to the Skype forum:
Go to the Support Network where other experienced users might be able to help.