I'm assuming the fact there's no automatic login for English.SE, etc. is by design.
By "automatic login" I mean when a banner slides down saying something like "You've been logged in. Click here to refresh"
It should work on all (non-meta) sites; however, it will only try once (otherwise the check would run everytime a not-logged in user visits any page). So if you visit english.se, then log in to diy.se, then go back to english.se, it won't try to auto-login again.
The login page is an exception -- it will always try there. Does it work on the english.se login page?