It is a common occurance, once an animal is shot, to see the animal run away. The hunter will go to where he/she thinks the animal was struck and look for blood sign. If there is no blood, the hunter will assume the shot was a miss. More blood indicates a more deadly shot which equals a shorter distance to find the animal. When shot and if able, the animal will run until they reach what they feel is a safe distance, then lie down. If the game is mortally wounded they will usually die in that spot.
Depending on how much trail sign is available, the animal can be VERY hard to find. I have heard of standard dachshunds being called to help track big game that has been shot and lost.
Concerning the "find a buck" problem, I do not know why you would work an area search-type problem, though. There is almost always a point of last known location to start from. And I would assume there is blood to trail, as well, if you believe the game is injured.
I'm not trying to be contrary, just pointing out that it would look more like a trailing problem than an area search in a big-game hunting situation.
I guess for "find a duck" it is a bit of an area search, but even then, ducks (and most other fowl I know of) are shot with a shotgun and limit the range you need the dog to travel to about 150-200yds? And the way I've seen them train is to go out on the line the hunter sees the fowl fall. A well trained field lab will travel for several hundred yards in a straight line through brush and over water until he smells the kill, or thinks he should, and then he'll start casting.
If you are really training to do a classic area search of 200-300 acres, using a bringsel, I am sincerely interested in hearing more about your training. I like the idea of the bringsel, but do not know enough about it to start training with one. Also, I think there are a lot of things hunters teach we can learn from, and I try to be very open minded, especially when I see good results.
Please keep us updated on what you learn!