How do I resolve 'We could not authenticate you' error during Facebook login with two-factor identification?

I use two-factor identification for logging on to Facebook. Recently after I receive the code from Facebook and enter it, I frequently get this message, even though almost no time has lapsed between the time I receive the code from Facebook and enter it.

"We could not authenticate you. This might happen if too much time passed after you began authentication flow. You will be redirected to the start of the flow."

Sometimes if I wait the required 3 minutes, then request a new code and enter it, I'm allowed to log in. Sometimes I get the same message again. Right now I'm in Facebook jail--I don't get their code at all.

[Re-Titled by Moderator]