There have been a number of users reporting this starting as early as google chrome 11.0.696 on Lucid Lynx. I am seeing it currently on chrome version 16.0.912.75 (Official Build 116452) on Oneiric Ocelot.
Despite having the cookies setting set to allow all cookies, and the "clear cookies on shutdown" option unchecked, All cookies (and sessions that rely on cookies to be persistent) are cleared. This makes using the browser very tedious if you (like me) shut down the browser at the end of the day.
I am currently looking into the 'bug' status of this; However if there is a workaround I can apply in the mean time that would be great! Or if anyone has any further information as to the cause of this bug (I am aware not all users are victim to this behaviour).
To better explain the issue I have created a small video (don't mind the slow internet connection) which can be seen here