It would depend on how fast you heal. When my healing was first coming in, it wasn't fast enough to stop my femoral artery from bleeding out, and that would have actually killed me.
A few weeks ago, I died at least six times that I'm aware of. Or re-died, I suppose, since I'm a vampire still. The terms are complicated.
I'm still here. But my healing factor was one of the best in the place I came from, and we're known for coming back from even a small handful of brain cells, assuming our skeletons are around to attach them to.