I didn't deer hunt until Indiana legalized hunting them with handguns. I borrowed a S&W 629 from a friend and loaded it with 180 grain HP ammo. I shot a buck at about 10 yards and dropped it right there. After it wallered around a bit, then laid still, I started climbing out of the blown down tree I was sitting in. When I made some noise, the deer came back to life, jumped up, and ran about 50 yards across a clearing where it bedded. I sat down to give it some time, but the neighboring land owner came driving back on a logging trail to cut wood. As he drove near where the buck had bedded I saw it get up and run. When I checked where it had bedded there was lots of blood, and I thought I would be fine. I gave it an hour, then began trailing the deer, but lost it after it went about a mile and went into Sugar Creek.
I quickly learned that I did two things wrong on that deer. I used an improper bullet not designed for hunting, and I shot the buck in the shoulder, where the bullet I was using failed miserably to penetrate.
Since that time, I switched to Winchester Premium Partition Gold ammo, using a Nosler 250 grain partition bullet, when I can find them, or I hand load Hornady 240 grain XTP's that are also designed as a hunting bullet. I also shoot behind shoulders, using the same aiming point I do with my bow.
Since loosing the first deer I ever shot with a handgun in .44 Magnum many years ago, I have shot a couple dozen or more with .44 magnums and have never had one go more than 40 or 50 yards. On only a couple of occasions have I had one go down on the spot.
The 284 pound field dressed buck I heart shot this year is the largest deer I've ever shot with a .44 magnum, and was the first I've not had a complete pass through with a 240 grain XTP. Shot at 30 yards with a Marlin rifle with a 20 inch barrel, the bullet destroyed the buck's heart, and liquefied its lungs, before it came to rest under its off side hide. I was able to pop it out with my knife. The bullet had expanded perfectly and had not come apart at all. The buck went about 40 yards. A few days later I shot a doe from the same stand at 40 yards with a S&W model 29 with a four inch barrel. The bullet completely penetrated the 120 pound doe, destroying both lungs. She went about 30 yards.
I'll continue using the .44 magnum in a rifle and a handgun until I can no longer hunt.