It took me two goes and then a two year wait in a holding pool before I started with BA. Try again in a year, it is worth it. Perhaps try getting into another airline in the meantime, that's what I did.
I have to admit though, it's pretty cheeky of them to ask for feedback after rejecting you. I would suggest you fill it out constructively. The fact that you've bothered to help them out, even after rejection will show you are a reasonable person, it should stay on your file if you keep the same email for your next application. It could make a difference for next time.