In our town, the code enforcer has to investigate all complaints and tell you to change your ways, but they don't have to cite you.
As a complainer this has occasionally been annoying to me--the neighbor's violent dogs kept jumping the fence into my yard and not letting me out of my own house. However, if I were ever in your shoes I think I would be able to politely nod and say "yes, sir" and then do as I pleased--maybe a little more discreetly.
If there are many other unchallenged infractions in your town, I might really try to just move them indoors somehow--a shed or garage or something. It doesn't seem like the officer is that interested in bugging you, the complaint just tied his hands.