Aatrox's main problem is that his kit is completely binary. If you have bigger numbers, you win - If the enemy has bigger numbers, he wins. His entire kit is built around stat checking opponents and hoping you've got the bigger numbers.
Aatrox suffers from that because his base numbers are embarrassingly low for a fighter. He's likely not winning a stat check unless he gets fed first, and it's difficult to get fed if you can't win stat checks with Aatrox. A vicious cycle.
Riot purposefully made it this way, since if you have an opponent who constantly forces stats checks and has the base stats to actually win them, it's not going to be a very enjoyable game for you. He's just going to all-in you every chance he gets, and has a better chance of winning that all-in every time he wins. That type of hyper snowballing is one of the mains reasons people don't like certain bully champs, as well as the current meta itself.
Further compounding the issue is that Aatrox is a drain tank. So the more damage he builds, the more defense he has by way of constant healing. This multiplies his snowballing problem since he can get ahead on offense and also get ahead on defense at the same time as long as he's attacking something. He's doubling-down on an often toxic mechanic.
In addition, Riot has traditionally been very bad at handling drains tanks. This is why WW was Urgot tier for the last couple years (except 4.20 Warwick, may he burn in hell), Xin balances on a knife's edge where one small buff or nerf could easily take him into broken OP or garbage respectively, and Olaf has the act of completely destroying a champion with nerfs and keeping them there for an extended period of time named after him. Even Aatrox himself was strong for all of a couple weeks back in season 3 before his kneecaps were broken and the balance team tried their hardest to forget he existed.
Those are his main problems. They refuse to be solved with simple number changes, so it's going to require a rework of how he functions on a basic level.