I've only killed 2 rabbits (one cottontail, and one jackrabbit). But both were taken with stone points. The first was the jackrabbit, and I shot it at about 12 feet with a small, mini-clovis shaped arrowhead. It went through the chest, sliced the side of its heart, and knocked it over. The rabbit squealed, kicked, then righted itself and ran in a large half circle. I waited about a minute, then followed the blood trail (yeah, that's right..the blood trail!). As soon as the blood trail started to dwindle, I looked up and there was my jackrabbit, laying dead behind a sage bush.
The second rabbit was taken at about 12 yards with a point made from the bottom of a beer bottle. I missed the first shot and the rabbit ran under a juniper tree. I threaded the second arrow right through all the branches, hitting the rabbit in the lower back on the right side. The point came out right behind its left shoulder. I ran up to the tree and that rabbit wasn't going anywhere...he just kicked a few times, then quickly died.
I did shoot a cottontail with a blunt, but hit it in the guts....it ran with the arrow hanging out of it and disappeared into some rocks. I never found that rabbit. I also shot a small cottontail with a stone-tipped rivercane arrow this summer, but I also hit that rabbit in the guts. That arrow zipped right through the rabbit, and he ran off into the brush and I never found him either.
So I think its about shot placement...the ones I've shot with stone points, as long as they have been in the vitals, are very quickly fatal.