Root password stopped working

I used to be able to enable “root” user and log in under it.
(I know this is not recommended but let's just assume there is an actual reason for doing so.)

I just repeated the instructions, set another root password and logged out of my account.

However, logging in with root user and the password I typed doesn't seem to work.
The login screen just shakes as if the password is incorrect.

I already tried setting it to a different one, then to an empty string—nothing works.
What do I do now?

Assuming you have followed these instructions and still can't get it to let you in as root, I would recommend trying out the instructions in this support discussion to get it working.