When Riot leaves a champion in a bad state for too long
What happens is it compounds the champions downward spiral into irrelevance.
With Aatrox for example, because no one ever plays him, his team doesn't know what to do with him. They can't make a marginal judgement call with him because they don't have enough experience to do so.
They think for example, that being down 2 kills in lane is already a lost cause to gank. They hesitate to go in with you in a fight when you have low health because they don't realize that the lifesteal and revive will buy them the time they need to win the fight.
As Aatrox is, if he was seen more often, he would have a higher win rate. He really isn't as bad as people think, and since very few people have ever mained him, most what you believe is really just hearsay and a few observations of him. Until you have played 500 or more ranked matches with him, you really have no idea what are you talking about.
He IS in a bad state, but not so bad that he can't carry or at least do very well in matches when the team doesn't treat him like some pariah and actually try to work off of what he has to offer.
So that is what Riot has done to him. Left him alone so that he can do even worse than he normally would have with his stats as they are.
Shame on you Riot. You are in charge of one game, supposedly hire smart bright people, make TONS of money and yet you don't have the resources or creativity to make sure no champion is left behind for 2 years? That is totally unacceptable, and whatever person in charge or policy or mindset that is in your company that is causing this is the same reason why eventually a better company will make a better game and you will become as irrelevant to MOBA's as Aatrox is right now to League of Legends.