Revan
Songster
Does your neighbor also free-range her birds? If so, then I am leaning towards some sort of poisonous plant that's in that area, especially given the length of time this has been going on and you still have birds, and that birds dying is not just isolated to you. Not to say that I am ruling out a disease, but poison seems to be a likely culprit. I am unfamiliar with Arizona plant life, so you'll need to take a look around and see what sorts of plants and shrubs are in your area and look-up online if they are poisonous in any way. If there are any, unfortunately you may have to stop free-ranging and build a large chicken run instead.