I say... if she is running away, let her celibrate her birthday without you intruding on it.
If she hasn't been calling, and you contact her on her birthday, there's a good chance she will see it as an intrusion.
Do you or do you not want to show her you can let go? Or will you make her fight you to let go right up until your final divorce hearing?
It's interesting how people are different this way. My W could care less about birthdays. If I had to do this, it would have no effect one way or another.
