We tick 'Remember Me' when logging in, but are forced to log in again when the browser sessions closes.
This is happening to all of our users, regardless of whether they log in with Google Apps or the native Atlassian login credentials.
Happens on both Firefox and Chrome, and cookies are enabled. I see that there have been some changes to the 'Remember Me' functionality in recent releases. This started happening about a week ago -- perhaps it's tied to the latest release?