Wordpress forces non-ssl login in described circumstance even though FORCE_SSL_ADMIN is set in wp-config

[geomouchet]

Wordpress provides an http login page in this circumstance:

1. Put the following in wp-config.php: define('FORCE_SSL_ADMIN', true);
2. Log into your Wordpress site via wp-login.php with an admin login.
3. Click Visit Site (home icon) at the top of the page.
4. Open a new brower tab.
5. Log into your Wordpress site in the new tab via wp-login.php.
6. Go back to previous tab.
7. Click on Edit Page.

It then displays the login box with http instead of https. (Ideally it would not require a new login at all, but instead would use the session from the new tab.)