You won't be able to do it natively.
But you could be clever and use web sockets (if you need 2 way comms) to continuously save the form data (just like this website does!) - or just use a vanilla Ajax call onkeyup - then save it in the PHP session, to be echo'ed out later.
Or a more straightfoward pluggable approach would be to use a library like jQuery Save as you Type
In either situation, it would save the form contents and allow them to visit another page and come back. The only thing you might have to do is retain the accordion position - but I'm not sure many customers would mind hitting "next" a couple of times if their data was already saved.