This game is addictive! I did notice that the player falls down when you're not moving, which presuming you're using rigidbodies, as you are using Unity, you can fix this by unchecking Use Gravity in the inspector :)
Congratulations, this is great!
Or you can put the mass at 0 in code
Thanks for the feedback! Initially, I thought of making a permanent drop, but what you noticed, I'll be happy to fix.