Make sure the box in the picture is checkmarked.
What browser are you using? Check to see in the browser options if there's a feature enabled to delete all cookies when the browser closes; if so, disable it. Firefox has a feature like this.
Also trying deleting all your cookies, exiting, and openning the browser again. Try logging in to RS again.
edit: wait, are you saying whenever you go to RS, you don't say logged into the RS WEBSITE? Or, are you saying whenever you go to RS, you don't stay logged into the VISTA desktop?