Rather than looking at it like you're being victimized, focus instead on the positive. Your coop and run are inspected - maybe more regularly than you'd like - and they've never found a problem. That makes you a wonderful ambassador against the "chickens are nasty, dirty things that don't belong in urban backyards" mentality. That also means that you would be a credible spokesperson if a campaign to eliminate backyard chickens in city limits rears its ugly head, as it has in other communities. It's quite possible that visiting your coop and run setup is something that the animal control officers don't mind doing after all of the other horrible things they see in a day - after hours of checking up on animal hoarders, puppy mills, and other atrocities, your place must restore their faith in human beings as compassionate and caring folks who can and do take proper care of the critters they have. Like a breath of fresh air to them!
As a town official here myself, I can tell you that being called Nazis and Gestapo and other such names just for doing what we are told to do hits kinda hard. What if you had a complaint and the officials didn't follow up on it? Would you be angry that your concerns were dismissed without action? It's been my experience that the "victim" of these complaints sees the visits and the paperwork as horrible intrusions - unless they suddenly have reason to file a similar complaint. Then they watch to see how long it takes the officials to get over to the neighbor's place, in some cases actually timing how long it took!
So it's an inconvenience, sure. It's also frustrating that you have someone in your area who holds such a grudge. But believe me, it's not the AC agents with the grudge - they just have the clipboard with their instructions on it. If you can, next time they show up go out there with a smile and good attitude, thanking them for their concern for your animals and their diligence in acting upon complaints. Or if their work hours and yours coincide, then take a minute to write them a nice note telling them you appreciate the way they've done their job while respecting your property and showing their dedication to the community they serve. Tell them that you regret that they are called out so often for no reason, and that you are proud that they have found no violations. They already know you show that same concern for your chickens so you have common ground. Won't be long before the next time a complaint from the same neighbor comes before them they'll say, "Oh, we know them, and there is no problem there." Good luck - oh, and congratulations on the great care your birds are getting......all of those visits and not a citation one is a giant pat on your back!