Tonight I completely lost my OpenID and credentials to sign in to stats.SE and math.SE. I was also unable to "recover" them via the "Recover" link on the myOpenID web sign-in and that site does not provide any support whatsoever.
Apparently, I'm not the only one.
I'm suspecting this will be happening to other stats.SE users and so this is why I'm posting this information here.
The fix is to simply sign up again for an account with the exactly the same information as before. Without needing to do any additional confirmation, my credentials were reestablished and my SE accounts were linked to everything properly.
This bug is not Stack Overflow / Stack Exchange related as far as I know.