There is no such limit for MIA and I speak from experience on both sides of the counter.

FLL and MCO have 4-hour limits but most stations—MIA included—will accept baggage on the day of departure regardless of departure time. Do note however that if you check in sufficiently early your bag may be sent on an earlier flight; be sure to use the baggage tracking feature on AA.com or the mobile app to know for sure.

That being said, MIA will definitely not accept bags the night before, nor will most (any?) stations since it's technically not allowed.