I think all game animals get pretty smart about that. I used to have my best luck with rabbits hunting right along the outside of the state park boundaries, where they were relatively easy to approach. And everyone knows how docile the wild ducks act, when they are on a pond where they can't be hunted.
Mourning doves in my back yard aren't afraid of me, but just try getting close to one out in the wild. They usually light out 100 yards ahead of me.
F.E. Warren AFB has a substantial antelope herd. The population explodes at the start of the hunting season. While on base, they're pretty relaxed. I walked through the middle of the herd from the Ops building to the BX during my lunch break several times. They stayed just out of reach, but weren't "spooked."