It depends on circumstances. If I was SURE I had not hit on the first shot, I might consider not shooting again. If I missed but I had some idea why I missed, that would enter into the decision. If I hit high because I held high, overestimating range, I might adjust and shoot again. If I missed by a big margin, maybe I would not shoot again because I might suspect my scope zero was moved or maybe that I was just not capable of an accurate shot then (out of breath, mist beaded up on my eyeglasses from heavy perspiration, other reasons).

On the other hand, if I wasn't sure I had hit or not I would keep shooting. This past October I shot at a running cow elk, quartering towards me. She was running but not in a full-out sprint, at least as far as I judged. I shot three times and did not notice any reaction whatsoever from the elk (.30-06 180 grain Remington Core Lokt). I thought I must have been hitting, however, as I did not think the shot was particularly difficult.

When I found her dead, not too far away from where I had shot her (maybe 100 yards, maybe 50 yards from where she stood when I first shot at her) she had two solid shots forwards in her left shoulder (would have exited diagonally out behind right shoulder), well placed. One of the two bullet holes looked kind of big, as if two shots landed pretty much within a half inch of each other (and hence, in this possible interpretation, all three shots landed -- I'm not making that call however: could be bone was hit by bullet and exploded outwards, creating an enlarged or oblong hole). The elk was hard hit and bled a lot. Yet I observed no physical reaction from her -- she didn't flinch, she didn't jump, she didn't speed up, she didn't slow down.

I definitely would not want to wound and have to trail an elk. Thus, if I might have hit, I will keep shooting -- hoping to drop the elk where they are. If I was sure I had missed, I would have to evaluate. I am not keen on taking long shots on elk, so that is part of my thinking and decision process. I ought to be able to make the kind of shots that I restrict myself to.

I also agree that if I shoot, definitely miss, and the animal starts off running like heck, I will not shoot. Generally I do not like shooting at running game. The cow elk above was a different story. I was very well set up and collected, she was not running in a sprint, the shot felt comfortable. Based on the result, I feel vindicated in my decision. Either one of the two hits was a killing shot.