When I started to play the whistle I could play notes in the first octave easily but had difficulty consistently hitting notes in the second octave. Then I learned how to control my overblowing well enough that I could hit at least the first half of the second octave consistently, but soon found I had the opposite problem: It was difficult for me to return to the bottom half of the first octave, especially D and E, after playing long passages at the top of the staff.
Then I read a tip on the web somewhere -- and I can't find the link, or I would give credit -- which helped tremendously. It's just a small conceptual shift, but it made a world of difference to me. When playing low D and E, exhale rather than blow.
I don't think I've missed either note once since I read that.