It seems like you don't have much to lose by asking. I do think it's okay to politely push back a little. I don't think you would be making them feel bad by saying that you're upset about what happened and really don't want to be terminated. (Plus it's kind of a harsh policy, so maybe they should feel bad about how it hurts people.) Obviously this is causing you a lot of distress, and I don't think that's the purpose of the policy. I wonder if you could try to explain why you have difficulty canceling when you need to and ask whether there is a different procedure you can use going forward (email or text instead of phone, etc.)

I'm also confused about the two no-show thing. Is that ever? Like if you're in therapy for six weeks or three years, you're out after your second no-show either way? It seems like a little forgiveness or flexibility is called for here...