Range/distance is much less a factor than the users ability with the tool! As Clint Eastwood/Dirty Harry said "A man should know his limitations!" I have taken deer at 500 yds. All of these shots had very mild winds. I would not have taken these shots if conditions had not been favorable. I have shot steel plates out to 1100 yds, many times making first round hits in what I would call normal conditions - windy but not terribly so. If I miss on a steel plate, it is easy to adjust and make a second round hit. When the target is an animal, I first assess the situation to determine my chance of making a first round hit. I then determine whether to take the shot based on my assessment. I have passes on some, but so far have not been wrong on the shots I did take.
A man in a club that I used to hunt in shot a deer at 100 - 125 yds. The deer went down on the first shot. He had seen deer run off after being knocked down on the first shot, so he chambered another round. The deer got up, then went back down when he shot. He chambered another round, same result. He shot 5 times, the deer went down each time, and finally stayed down the last shot. When he got to the buck, he found his first shot had hit him in the hip and fractured it, which is why he kept falling down. The last shot hit the deer in the shoulder and kept him down. There were 3 misses. This was at a range that most people would call acceptable, but in my opinion was not for him. When he told the story at the camp, I think I hurt his feeling when I told him he needed more trigger time at the range! The rifle was a Remington 700 chambered in 7mm RM.
If you don't take the time to learn to be proficient with your tool then the range you are shooting simply doesn't matter, you will not be successful. I did go to a long range shooting school (Bangsteel.com) where I learned a lot and became proficient very quickly. I continue to practice shooting a far as possible locally. I go to F-Class matches primarily for the practice of reading wind and shooting long range. If you can put 80% of your shots in the 10 ring you are doing pretty well as a hunter. You learn about reading wind from the 20% outside the 10 ring.