Only reasonable and canon answer I can think of is: the reason he survives that fall from space is because his suit locked up. Maybe 20 feet isn't a high enough height aka doesn't give the suit enough time to lock up.
Because in halo 1 and Halo: Reach Spartans (master cheif, Noble 6) wore mark 5 armour. In Halo 2 cheif got mark 6 armour that has shields that can take a hit greater than his terminal velocity (they will protect him no matter how far he falls), so he could just survive the fall from space. Also they just added fall damage for balancing reasons.
in halo 3 multiplayer you play as spartan-'ll's with Mjolnir mark 6 armour in halo reach you play as spartan-lll''s with mark 5 armour, but thats not why, noble six also survived a fall from orbit because he ha time to lock his armour and absorb the impact, with a short fall theres no time.