In a perfect world, a predator would bite the ground every time we pressed a trigger. Certainly the guns and ammo we use are capable of dropping predators in their tracks. Of course, that instant collapse doesn't always happen. Not only because we sometimes miss completely, but also because our shot can be less than a surgically precise hit. If that hit is too high, too low or too far back, the animal might go only partially down or react in some other way to indicate a less than immediately fatal hit. When that happens, at what point do you shoot again? This is an important question, especially if you're going to market the fur, as too many holes in a critter can make the hide worthless.
When it comes to coyotes, I always tell any new hunters that if a coyote has two or more good legs under it after the first shot, shoot 'em again. In reality, that means if the animal isn't horizontal, fire another shot. I've seen too many coyotes that people believe to be mortally wounded, run off and disappear. It's a lesson I've learned the hard way.
A common situation is what's sometimes referred to as a death spin. After a shot, the coyote starts biting at that "thing" that just hit it in the side. It ends up looking like a dog chasing its tail and can go on for several seconds. If that "thing" hit right behind the shoulder and took out the back half of the lungs, the coyote's behavior is indeed a death spin, and it'll expire quickly. However, if the hit was too far back, the coyote will soon stop spinning, start running and disappear forever. Do you shoot again while it's in that spin and risk damaging the hide of a dead coyote, or wait 30 seconds for it to collapse? It all depends how confident you are in your bullet placement.
This coyote took a hit from a .243 Win. and ran off to expire in a burrow under a large pile of logs. Recovery meant crawling in after it, but a second shot would have prevented that unwelcome task.
Last year I was hunting with a friend who's had his share of trouble hitting coyotes. When a 'yote he shot immediately went into the aforementioned spin, I quickly put another one in it rather than risk losing the animal. It turned out his shot demolished both lungs and my shot wasn't necessary, but I wanted to be sure, so I shot a spinner. On the other hand, a coyote I called in early this year came within 30 yards and stopped broadside. I deliberately shot it through the lungs and it ran off about 40 yards before piling up, stone dead. I could have shot it again during that run, but I was totally confident in where my bullet went, so I let the 'yote do a short death run. If more distance or some other factor would have made that shot more difficult, I'd have kept throwing lead until the dog went down.
In the end, when a hunter stops shooting boils down to a personal call. However, remember that two-leg rule. If that predator has still got two legs under it after the first shot, shoot 'em again.