https://matchhistory.na.leagueoflegends.com/en/#match-details/NA1/3105603063/39173459?tab=overview
Aatrox's items that game;
vs your AP leaning squishy team. There were a couple factors keeping Aatrox in the game here.
-You let him get fed
-He build to buff his healing which included;
INNATE: Aatrox periodically empowers his next basic attack to gain Range icon 50 bonus range and deal* 5% − 12% (based on level) of the target's maximum health as Attack damage bonus physical damage on-hit, capped at 100 against monsters, and Heal power healing him for the bonus physical damage dealt.**
15% Healing on all damage 
30% increase on all healing 
UNIQUE – LIFELINE: If you take 400 − 1800 (based on level) damage within 5 seconds, you gain a shield for up to 3.75 seconds equal to 75% bonus health, which start decaying after 0.75 seconds (60 second cooldown).
(THIS ITEM IS AMAZING VS BURST CHAMPIONS LIKE YOUR AKALI AND MANY AP CHAMPS...)
reducing your already very low armor buffing his damage vs you, and thus healing even more.
now reduce that bu 40%, and it's still a massive amount of healing, and you have to overcome his shield and magic resist all within your own cooldowns because you're a burst champion that should be focusing the enemy back line, not the front line diver called Aatrox.