In reflection on my history with AH, these moments occur for various reasons. We find ourselves having to stop and think about our reactions -whether to listen to them or not - trying to guess at the right answers. What does that tell you about the relationship?
The rest of the world doesn't know what we go through and cannot see situations through our exp. They know what normal is and our sense of it changes living with them.
Something in the relationship took you to the point of separating and no contact - remember why. I agree with something mentioned earlier - do any of his contacts begin with "I am sorry" / "I messed things up"/ "I want to make things right" followed by what he will do for you?
I do understand the anxiety about the BD so close to the break up. For two years through our separation and on/off contact I have sent a card. The reason for it is this: we are still married and see each other everyday- if I wasn't married I wouldn't send one. BTW - he did not ever remember my BD through all this. This year I will not be sending one and it will be strange but I am not wasting my time.
I do like the suggestion of buying yourself something with the money you would have spent on him. Buying him a card or anything only keeps him in your life and is that what you want to do?