If you check the "Remember my login." box, the cookie will stay for 5 days. Each time you access the Command Center, the cookie is renewed for another 5 days. If you click the Logout link, the cookie is deleted immediately.
Do NOT check the "Remember my Login" box on a public computer (such as at a library). Anyone using that computer would then have access to your account.
Even if you check the "Remember my Login" box, if you do not access your Command Center for five days your login session will be forgotten, and you will need to log in again. If you click the Logout link when leaving your Command Center, your login session will also be forgotten.