Unless you've ticked the "Remember Me" box when you log in, it should automatically log you off once you've been off the site for a while. Anyway, unless you're using a public computer or one of your family members uses CYS as well, staying logged on isn't really much of a problem.
I've been unable to log off before but it was a temporary thing. Try deleting your browser's cookies or cache or something, that usually fixes things like this.