Log out link wont disappear

I run a ecommerce site and when i click the log out link within my header on my main home page it takes me out of the secure ssl side and logs me out and with the log out link changing to log in as it should, but when I try to view a product or another page, the log out link reappears. when i click on in it takes me to the home page with the log out changing back to login. this does this with whatever page i click, or if i log out under another page it other than my home page it takes me back to home with the log out changing to log in, but once i click another page the log out button comes back, never seems to make the log out link disappear. Please help?

https://www.ads-software.com/extend/plugins/w3-total-cache/