Compatibility issue with CAPTCHA module

I am currently using Login Destination 5.x-1.1 on my Drupal 5.6 site. I also have the CAPTCHA module, version 5.x-3.1.

The problem I have experienced is that when a user attempts to log in but enters the wrong CAPTCHA code, the login destination redirects them to the specified destination, instead of holding them on the user login page.

The "incorrect captcha code" error message is still displayed on the destination page, but the user then has to navigate back to the login page to try again.

I'm not certain whether this was is more of an issue with Login Destination or with CAPTCHA or just an unfortunate sideffect of the integration of the two but I am raising it here first.