Could also be some module malfunctioning staying on. Called parasitic draw. Even though the car is off, a lot of systems (modules) can still be on. Biggest one would be your Body Control Module. Easiest way of finding how much current is being drawn is with multimeter in between + cable and + post. Remember, checking current is done in series unlike voltage which is parallel.
Another thing, batteries and alternators almost go hand in hand, as the battery weakens, the alternator is stressed harder and harder to charge the battery and a weak battery can cause alternator failure.