Before you fully discount the caliber I'd say we would need to look at the variables first. The deer was already freaked out and pumped full of adrenaline so even with a lethal hit through the vitals (with any pistol caliber) I would still expect her to stay up for a little bit. I have personally killed both deer and hogs with a 9mm in the past. One deer at almost 30 yds shooting 124gr speer gold dot +P hollow points. The bullet entered behind the left shoulder, turned a large portion of the lungs/top of heart into jello, and exited through the off side shoulder blade. He took one jump at the shot and rolled over dead right there.