No no… Don’t blame yourself. You did nothing wrong here. Very scientifically speaking we still have no clear answer on how the sexuality of a person is determined. So far there is a consensus that there is a biological factor also in play.
It is not your failure as a partner. These are things beyond your control. She also can’t do much on this. Therapy won’t change the underlying reality. It will just help you to cope up with the hard realities that you are facing.
I highly recommend you take individual therapy if you haven’t done so far. You may have to untangle decades of experiences to get in terms with it. It’s never late, and the right therapist will definitely improve how you handle this.
I would say exactly that is what you have to describe. As I said certain things cannot be changed with therapy. It can only help you to get in terms with it.
Regarding the last point you mentioned. You are not giving up on her. Exerting constant pressure can’t change certain realities. It is like thinking you can drain an ocean with a bucket and a lot of time.
You have to accept that there is nothing ‘wrong’ with your partner. If she is asexual there is nothing to ‘cure’. You must build your life around this fact to be happy.
This does not mean that your needs should be discarded. In the same way you accept and respect the fact that she is asexual, she also has to take a mature stand and work on finding common grounds or compromises. That is how relationships work, isn’t it?
You start therapy. Remember that you will need to find a suitable therapist. So don’t hesitate to change therapists until you find one you are comfortable with. Maybe the therapist can help you on how this topic needs to be discussed with your partner. That may slowly open up new ways to improve the conditions.