Yes, as soon as he is moving downwards you can boost again.
I kind of liked that … Otherwise how would one be able to do the Jumping Jack Flash level :)
One idea would be to add a power meter that depletes, so that you can only jump max 3-4 times and then it will recharge if you are on the ground.
I was thinking make it so you only get one double jump, but hitting the wall brings it back. I haven't finished the game, but I think that would get you through all the levels I played.