Sharing feedback is a huge risk for companies. Giving feedback after a rejection provides them ammunition for a potential discrimination lawsuit.
For this specific case, your best bet is to follow up with individuals after the interview, and ask for very specific things, rather than asking someone in HR.
One good way to ask for feedback has been to ask, "Is there anything that is giving you a pause for concern, or anything that gives you uncertainty about continuing the process?" The best time to ask is as the second question after the interviewer asks, "Do you have any questions for me?".
When you get a good response from that question, it allows you to confront your perceived weaknesses. At worst, it tells you something you already knew, "You could have solved the white board question in N time."
Getting good feedback is hard, both for the person to give, and for the asker to receive and process. Don't take it personally that people don't want to give you feedback.
