I know if you log out it will clear all catches related to the site so by logging out it will ask you to logging in and will make you check the box. It's a security reason as otherwise by having that as default setting when visiting public computer and visiting the site, you could accidentally leave yourself signed in and the person being admin could have devastating results.
What comes to www. in the beginning of the website. I wasn't even aware it allowed you visit the site with that in the end and I have no idea how that works exactly but I'll take a look at it later.
UPDATE:
I checked that out and it seems that with www. in the beginning the site doesn't work properly. If you click on any of the forums thought it does show you're logged in and remove the www. from the beginning. To be honest I don't even know how www. in the beginnig works as that is not our registered website
Thanks: 
Originally Posted by Simba The Mighty
I know if you log out it will clear all catches related to the site so by logging out it will ask you to logging in and will make you check the box. It's a security reason as otherwise by having that as default setting when visiting public computer and visiting the site, you could accidentally leave yourself signed in and the person being admin could have devastating results.
