The problem with Team Rocket has and always will be their desire to catch Pikachu and deliver him to the Boss, Giovanni. Unlike Ash's goal to become Pokémon Master, this is a goal that has one step and that one step will never happen no matter how hard they tried. Catch Pikachu and deliever him to Giovanni will either end the show on a downer note or spell the end of the Team Rocket organization (as Ash will move heaven and earth to get Pikachu back).
Because it's a one step process, Team Rocket cannot become better. They can be better in contests or side jobs or a radio show, but never in their main profession of stealing Pokémon (especially Pikachu). And they always throw away the things they are good at for a goal that they will never succeed in. Truly static characters.
Team Rocket worked back when Ash was a rookie and immature trainer surrounded by friends who often bicker with him alot. Ash, Misty and Brock... they're best friends but they do quarrel over directions, training methods, and food. And their quarrels offers a lot of unique chemistry when Team Rocket intervenes with their own relationship chemistry. Recall how Misty called Jessie an old, ugly hag and how Jessie raged like Vulpix. Or Meowth cheating in a Pokémon match by throwing water at Brock's Onix. Despite being incomptent, Team Rocket was on equal footing with the original trio.
But when the original trio parted ways, Team Rocket began to lose much of their antagonistic dynamic with Ash. Ash being on his own and later becoming somewhat of a mentor to May meant that Ash was maturing as a person. He was growing beyond the rookie he once was. May, on the other hand, had less of a reason to truly hate Team Rocket (most of her rivalry revolved around a disguised Jessie in Contests) and while Brock did come back, the cracks were showing in Team Rocket. Every time Ash got a new companion to travel with, the rivalry with Team Rocket became less and less organic. They just hate Team Rocket for simply being bad guys that annoyingly show up, not because of a long history like with Ash.
Meanwhile, Ash was growing to new heights and facing bigger challenges. He was fighting Frontier Brains, Elite Fours, and even Champions now. He was getting better while Team Rocket remained the same. Consequently, Ash could now just blast off Team Rocket whenever he feels like it. And this wouldn't be as a bad if it weren't for the fact that in the AG and DP eras, Team Rocket showed up in every single episode... and most of the time, as the villains. When Team Rocket go from unique characters to just mandatory obstacles, you know something went wrong for them.