I\'ve searched high and low for a solution to this, with no luck. My host told me they are too busy to help.
Magento 1.4.2 // SSL cert
Tinybricks excellent support helped us out. Thanks for all of your suggestions. This was a localized problem based off cache and a module called Lightspeed.
Is the session cookie being set to be HTTPS-only? That'll prevent it from being carried over to regular HTTP requests, effectively giving the user two different sessions.
We were experiencing similar issues where our custom nav (depending on whether a user was logged in or not, was not very consistent across different pages.
We followed the suggestion @ http://ka.lpe.sh/2011/06/19/magento-checking-customer-admin-is-logged-in-or-not/ to check if a user was logged base on the frontend session variable before a rendering a particular block, and it seems to have done the trick.
Perhaps you can try something similar.
You have in your screenshot two frontend cookie with two domains, one with www and an other one without. Check if you have a correct domain name in the configuration > Web tab > Cookie Management > Cookie Domain (or something close to that). If it's empty set it to ".mydomain.com" and try again. Check if you don't have different cookie domain in your configuration in the other store views, set them to "use website".
If still doesn't work, What are the values of the fields of cookie management and the cookie validation settings