PRPC has two kind of timeout. Browser and requestor, If we keep both the timeout alive then we can achieve that. So, one thing is to have no timeout at the browser level. Apart from that, the requestor timeout is by default is 2 hour. This is fine and passivation will happen. After that we clear passivated data after 24hr (when system cleaner runs). If we don't let the passivation data to be deleted then ideally we will save the session and we can achieve that.
Let me know if this works for you. I have never tried this though. It just a theory i am proposing.