West Warwick, RI
Its opening up HTTP sessions to the site, and then keeping them open for a length of time. This is normal. When you close the browser, the session shouldn't close, because the session isnt between the browser and the IP, but your computer and the IP. And even if you shut down the computer, the router will keep the connection open for a certain amount of time. That length of time is based on the traffic type. This is because of how TCP works. You should be able to see the session length (the 7642 number in pic) change if you F5 on the page.
Now if your saying your shutting down the computer that was browsing, and the session timer isn't changing with F5, I would say thats some kind of bug. Other then that, I really wouldn't worry about it.