Bama's defense got fatigued against LSU because they had a hard time getting off the field on 3rd down. LSU had the ball for over 39 minutes.
Since Bama's off week, they have had to play on the road at Missouri, on the road at Tennessee, at home home against a decent Mississippi State, and on the road against LSU. Since Bama's off week, they have had three out of four games on the road against SEC teams. Yes I'd say they are a little tired.