I have seen exactly the same thing, with everything from ruffed grouse to deer. My practice is to stop frequently, but only when I'm in a spot where I could take a shot. Grouse, in particular, seemed to only get nervous enough to flush after I have paused for a good long time. I made it my habit to wait about as long as I thought it would take and then give it a few more minutes. Often enough, just as I'm about to take my first step up goes the bird. Couldn't tell you how many whitetails I've jumped out of the heavy grass that grows along the tree rows separating the harvested sugar beet fields in northwestern Minnesota. As often as not I had already walked past the animals, and they did not go into the drive to where the standers were waiting. Some I turned and killed; others got away unscathed. Lots of times I was left wondering where the deer had been hiding, because I thought that I could see into the grass where it came from. These were probably the ones that laid their heads down on the ground. Overall I'd have to say that if there is enough cover to hide a bunny or a ringneck, a whitetail buck has more than enough cover to hide in.