I'm not sure what problem you're experiencing (that you haven't already solved). Please explain a bit more fully if there is a problem.

And now that I already made the post, an update:

It appears that every minute it asks me the Primary Password again, but pressing Cancel still works

I'm not sure what problem you're experiencing (that you haven't already solved). Please explain a bit more fully if there is a problem.

If I press cancel some times, the primary password isn't needed to log in in thunderbird, so everyone with the access on my pc can launch thunderbird, press cancel, and enter and see all my emails without any problem.

It's a very big security issue.

I still don't understand the problem. Do you have a password to access the Thunderbird program? Or is it the password to log on to your Email Account? If you are accessing your Email Account you would need a password so, if you think access is achieved without Thunderbird submitting it, you need to urgently contact your Email Provider.

Settings > Privacy & Security > Primary Password

It is the password to access all password saved in thunderbird AND to access thunderbird, the application.

So when I launch thunderbird, to access all the email, I need to use it. But if instead of entering the password I click "Cancel" for like 3-4 times, I can access to thunderbird anyway, without the Primary Password. So it is useless.

You don't need to access the stored passwords to access your email. And Thunderbird is already running when you get to this screen so you this doesn't determine the accessibility of TB.

I have been unable to duplicate the error. However, you may want to log a bug report here - https://www-archive.mozilla.org/support/thunderbird/bugs

I've now had a reply from a fellow Forum user who has advised me that this is a known bug. However, it's unlikely to be fixed any time soon. Thank you for pointing it out.

The primary (formerly master) password only protects access to the saved passwords. It does not protect access to the program or the mail folders.

http://kb.mozillazine.org/Master_password