Here the prepositions 'off' and 'down' are literal, not figurative. Here are some examples of use: 1. The apple fell off the tree. (The apple was on the tree...and now it is off the tree) A button fell off my jacket (There was a button on my jacket....and now it is off of my jacket) on...then off 2. Jim fell down the stairs and broke his arm. (Jim tumbled down a staircase) When you learn to ice skate, you fall down a lot. (When learning to ice skate, you fall on the ice a lot ) down is the direction the person or thing is falling

You have to fall off something, like fall off a horse, or fall off a wall. With fall down, you could simply fall down without the speaker specifying what it is you fell from. Let me know what object the person is falling from, so I can tell you which sounds better.