Session gone after opening a new tab within Internet explorer / Google Chrome

The whole session id and cookie persistence isn't applicable anymore because it is a result of the 302 error we get as response of the F5. Now the F5 does this for any object that isn't present on the website. Therefore we try to adjust the application to include the object in the section which is opened by a new tab. For the rest of the objects we try to figure out why the F5 does a redirect when the object isn't there. We allready set the rewrite option to NONE on the http profile. But there is probably something else we're overlooking.