Do you have you main installation on one domain and your second blog on a domain that is NOT a subdomain of the first blog? e.g.
First: mywordpress.com
Second: mysite.com — NOT mysite.mywordpress.com
In that case wordpress probably just is not able to set the cookie for the second blog. Try adding
define('COOKIE_DOMAIN', $_SERVER['HTTP_HOST']);
to your wp-config.php.