We are aware that sometimes some users will have to click "login" and will then be recognized without having to actually re-enter username and password again. This is a quirk that we will review and queue for adjusting if possible.
As for the cookie issue, as was correctly surmised, this could be a local browser phenomenon and could be impossible to diagnose from our end. Please check that cookie permissions on a site basis in your browser's settings are set to be allowed, and even logout and clear cache to be thorough. Then login again and try leaving and revisiting a couple times.
Please let us know how this works out, for anyone experiencing this or a similar issue.
Thanks,