Some USA carriers claim that the rule (vaguely due to security) is that you must retrieve the bag if the connection is over eight hours, but I've never seem people verifying the time at the post-customs bag drop if the bag is checked through. However, leaving the bag at MIA for so long risks theft from the bag as well as it being set aside and forgotten so that it doesn't make the flight. Depending on your arrangements for the night, it might be better to take the bag with you. [Remember that TSA basically doesn't let you lock checked bags.]