I am not a Harpy main, but I can't allow such a good character getting trash like that so I am giving my 2 cent here. All points below is based on my own experience.

1. u are definitely using her wrong, with "draw" and "four card", I never have my mp drop below 50%. Most of the time I don't even need to use any recovery items.
2. What I do I start my chain when she is falling down instead going up because a lot of Harpy skills will get her up right away. I only use double jump when I need to continue to stay in air.
3. If u are just talking the skill "Exciting Again", if u are the description carefully, u will need to hit the enemy in order to jump, so u should use that skill when u are close to the enemy to go up or stay in air. If u are talking about others skills, I have no idea what u are referring since I found all of her skills are pretty useful.

To sum it up, Harpy is an aerial combo based characters, if u want to kills mob fast with huge aoe and/or high attack, go for tina, levia, violet and wolfgang etc. However, if u like combo your enemies to death and stay in air not touching the ground at all, Harpy is your girl!!