Never with a bow, but two instances of having to finish the job with alternate means gun hunting back when I was younger. Once I shot a small buck on a deer drive. He was running at about 40 yard, shot was with 12ga OO buck. He dropped like a stone at the shot and was perfectly still until I was point blank - when I noticed his eyes were closed. A follow up shot from 5 feet with OO buck wasn't my first choice.

The other instance was a doe I shot with my dad's 30-06 from about 70 yards. The doe was standing at the edge of a stream and the shot broke her spine. She fell into the stream after the shot into almost waist deep water (banks are undercut). A follow-up shot into the water wasn't an option as only her head was above the surface and she was drifting slightly in the current. I ended her struggle without a knife and will use my pistol if presented with a similar situation in the future.