If the cookies for the 3rd party site are set then your P3P looks fine and you can navigate fine for over a minute without losing session then the problem must be something with the timeRefresh()
As you can't get a customized URL of the 3rd party site in order to issue a specific reload and assuming that you have no control over the third party site, I suggest you do something different. Set up some JavaScript to load an image from the site (the logo or something else that won't change, or alternatively a script or page) every minute from a frame that you have control over. Because the browser is the same, any existing cookies from a login will be referenced and it will extend the login.