Yeah, I think I made it too challenging. The trick is to flap sparingly and glide. If you hold the left/right arrows you will glide and fall less quickly than if you simply stop and only flap. You can also hold left or right and flap at the same time to ensure you don't dive bomb and lose height.
EDIT: The energy bar slowly recovers with time, but not fast enough to fly infinitely. There is no way to get more energy until later in the game ;)
EDIT2: You can skip dialogue with "s" as it says in the bottom corner, but maybe you are doing that already.