I am experiencing the same issue and want to share this with the community to inform all users. This is something highly concerning and unprofessional on behalf of the people behind Wordfence.
We are running a news website and we are locked out from our website because Wordfence does not send the sms with the code to login. The only way of support is to open a ticket, which he have done, and to wait.
This is the only reason we upgraded to the paid version of Wordfence as it is one of the main “pro” features. Unfortunately it malfunctions.