This bookmarklet reloads the page every 5min, almost certainly keeping the session active as if you had just opened a new tab; the trick is to reload the page in a separate window/tab as follows.
javascript:_x=setInterval(function(){open(location.href, 'otherWindow')}, 1000*60*5)
You will have to disable your popup blocker / allow the first window to open. Obviously only one new window is created, else this would be a terrible solution.
To test this, merely replace 1000*60*5 with something like 1000*5 (5 seconds).
The user didn't really need it for his use case, but if someone else wants to avoid closing the page, you can just use this bookmarklet to stop the refreshing.
javascript:clearInterval(_x)