Actually I've never met any business that will tell you why they are not giving you a job. In a way it's probably a good idea as most people would be more offended than assisted by the reasons offered. Not to mention opening the doorway to unsuccessful applicants coming back and arguing against the feedback offered.
Most of the time if I think back on the interview I do know where I was weak or possibily not suitable for that particular company. And I also firmly believe that when company rejects you they are doing you a favour. Most often it's because your personality or preferred working style will not be a good fit for their company culture. You would be unhappy there.
You may not want to hear that or even agree with it when you have been rejected for what appeared to be your dream job. But trust the people that work there, they understand the company from a perspective you don't and do know what type of people will be happy there.
I've often found myself in surprise positions with company's I would never have thought of working for. And almost without exception it's been a better fit for me than the job I initally thought I wanted.
Kepp going because BA just may not be a good match for you. It's almost certain there's a better employer who'll love working for more out there.