To the best of my knowledge, this feature doesn't exist. However, if you plan to go away for a bit but don't want to become idle so you'll get logged out, open a new tab or window and click on the
Currently Active Users link under "What's going on?" on the main page and let it stay open while you're gone. The site marks all new posts as "read" after about 15 minutes of inactivity. By opening that link, you're refreshing a page on a regular enough basis to prevent you from losing the info on the "New Posts" page.