I think the reason most clinics insist on their donors being anonymous is that they don't have/don't want to create a process for maintaining contact information and facilitating the contact. They just don't have the expertise in this area like an agency would.
My clinic originally said no, but after talking to the donor, we agreed to openness and put it in our contract. If you are in a clinic that insists on anonymity, you can consider some creative ways to try to make a connection to the donor. Ask if she would be open to receiving letters from you and if the clinic would forward them if you provided them in a blank envelope with postage. Ask if she would be willing to talk to you before hand. During that conversation, you could talk to her directly about being open in the future. Will you have a contract directly between you and the donor? If so, you could contact her attorney to see if s/he could facilitate a conversation or a future with some openness. Of course, there may be some donors who are insisting on anonymity for their own sakes, but if there is some wavering and the only reason it isn't there is because of the clinic, then it wouldn't hurt to try to find some creative options.