Authentication Captcha is not working when using an Active Directory authenticator

The following process describes how to reproduce the issue.

Tested on 12.10.4 and 12.6.6

These first steps are done on Chrome, non-incognito browser window:
1. The Captcha is enabled from the wiki administration > Authentication tab
2. Install Active Directory Application and add license
3. Log out of the wiki.
4. While on the login page, write the correct user name and the wrong password for 3 times and then Captcha should be shown.
5. Now, write the correct user name, the correct password, but the wrong captcha. A new captcha login should appear.
6. Try again to complete with the correct user name, the correct password, the correct captcha.
Expected result:
The login would be successful.

Actual result:
A new captcha login is shown.

Now, when going on a different browser, Firefox, private window:
7. Try again to complete with the correct user name, the correct password, the correct captcha.
Expected result:
The login would be successful.

Actual result:
A new captcha login is shown.

Back on Chrome, if tried to login with a superadmin, the login is successful, and while as superadmin, I disable Captcha from the wiki Administration > Authentication tab.

Then, on Firefox, a new window, tried to login with the regular admin user and now the Captcha login did not appear, but the login page was just refreshed:

One workaround was to uninstall the AD app and reinstall it back. After reactivating captcha the issue did not happen again. But this would not actually mean that it cannot happen again if the same scenario would be repeated by mistake by a user.

This issue is not happening on a wiki that doesn't have an Active Directory Application installed.