…Been there before. Hang in there. I wouldn’t compose questions until some time has passed. Also, since you made it to the second round, it probably sounds like your work was great but didn’t fit the company model. Sometimes, they need an exact fit to hit the ground running fast, and don’t have enough time/resources to mold you into the position. It happens.
If you’re really adamant to work there, stay on the radar. take 3 months off, learn more about the company and brand experience, and model an assignment for them. Remember to sell your process and demonstrate what potential they could have if they hire you.
Nose to the grindstone, keep going, play it smart, and persistence will pay off.