How can I improve my interview skills with HR?
Very simply, some people don't interview well, while other people simply aren't the right fit for a company's particular culture.
A bigger issue for you is knowing how you actually come across in interviews. You might want to go back and simply ask what wasn't right or how you can improve--because if you don't get that feedback or don't know what is "off"--you'll never truly learn how to fix or correct it.
Know also that people at the top are constantly looking for feedback and ways to strengthen their weaknesses and learn better techniques and strategies to communicate better--because better communication leads to better results. And if the pros can do that--you can, too.