When I login to wp-admin, I tick the box to "remember me", so I don't have to login again next time.
However, if I close the wp-admin tab, and reopen wp-admin in a new tab, I have to login again.
Alternatively, if I browse to another website, and then return to wp-admin, I have to login again.
This happens in Chrome and Firefox.
It doesn't happen in IE9 - in IE9 I am remembered.
In wp-config.php, 'WP_HOME' & 'WP_SITEURL' are set to the same value.