So, I kinda relate to what you're saying in the Ahri vs. Fizz matchup. In the early lane phases, you can harrass him and deny him CS pretty easily, but once he gets to levels 3-4, he'll probably ask for a gank, and also he'll probably be harder to deny due to having his Q, W, and E now. Once he reaches 6, you have to respect his ult range, and once he completes Lich Bane, you have to respect that he can kill you, even if he misses his ult.
I've given up on trying to kill Fizz at all in my games vs. him, and I realize that you can only roam vs. Fizz when playing Ahri, unless he's super bad. The good thing is that Fizz has a very low impact on the game even if he gets kills, and he most likely will get fed regardless even if you don't feed him. So, try to keep your lane pushed as much as possible, and then roam. He will also roam as well, but Ahri can do it better I feel. You can keep Fizz coming back to mid lane to push the wave as well, which will waste his time and give you the ability to roam bot or top. If your jungler and you both roam at the same time, you can catch Fizz out of position, since he might follow your roam, and then you can both kill him. I do not suggest trying to kill FIzz unless you have a teammate with you though.
Due to how slippery Fizz is, I would ignore chasing him if you get him low, as it just wastes your time, and that's what he wants, and he'll try to bait you to follow and lead you to one of his teammates, which is most likely his jungler.
I hate the Fizz matchup, but I prefer it over Yasuo, since I don't want Wind Wall in my games. Wish I could have two bans to keep both out of my games.