As a heli pilot (plenty of hours in previous games) who feels like a complete noob in the new game I've put some time into thinking about it and I'm not sure the issue is AA.
I think it might be due to playing with 2x the people we usually do. That means twice as many people that are running around with AA. I'm not sure how to fix something like that but it really does make playing the game as a helicopter pilot difficult. Between that, the controls feeling bad and the attack helo feeling like a sloth I can't seem to keep one in the air longer than 2 minutes and that's if I'm sitting way out on the edge of the map letting my gunner do the work.
I might just start avoiding them until something is reworked.