UPDATE:
My husband saw his therapist today and convinced him to rethink this policy.
He (the T) did not like this policy personally, but they needed something so they hired a consultant to implement this.
He says that he is not going to violate the policy for us or get rid of it, but they are going to have a meeting about how to adjust it so that it is fair and also does not create even more emotional distress.
The possible solution will be to allow people to write a letter detailing why they believe they kept missing appointments and what they will do to ensure it does not continue. That way it is therapeutic for the patient and also can contribute to the actual goal of this policy.
I see my therapist next week and we will see what ends up happening.