AB remembers who you are through the cookies that it places on your browser. It seems likely that you've got your browser configured so as to delete all cookies every time you close it (or, alternatively, you're using other security software which deletes your cookies).
Internet Explorer? Let's pause for a moment while most people here fall about laughing!
This explains how to control cookies in IE11
http://www.technipages.com/ie-enable-disable-cookies
(Note, in particular, that if you use the 'private browsing' option, IE will always delete your cookies at the end of every session. So, if you want to remain logged in on AB, make sure that you don't view the site via 'private browsing').