Hi Eddy
On the one hand you say that you don’t see the friendship starting up again. On the other hand you are still thinking about wishing her a happy birthday. It sounds like both of you are unsure where this could potentially go, and both of you are afraid of being hurt again.

Here’s what I would suggest:
Send her a birthday card. In that card, mention that you miss her. Tell her that you do not understand what you may have done that would upset her that much. Also let her know that she is in your thoughts and that you do appreciate all the good times you spent together as friends, and that you will always cherish those memories.

If she is interested in continuing the friendship, she will understand that you are being sincere, and she will contact you. If she does nothing, then take the good memories, tuck them away in a corner of your Heart, and accept that this is one of those relationships in life that was only meant to last a certain time.

Hope that helps!
Gunter