I have had one rabbit die in recovery from his neuter, due to complications from e. cuniculi. I had another almost die pre neuter after the anesthesia was administered. Both were at a low cost spay and neuter clinic where they don't intubate the rabbit and where they probably aren't as closely monitored post neuter, as they would be at a good rabbit clinic. The second rabbit, I did end up getting him successfully neutered by an experienced rabbit vet, that intubates for the surgery. He did absolutely fine the second time around, with no complications. I think his previous near death experience was due to not being intubated and having narrow nasal passages that may have been obstructed leading to his heart stopping. I have also had at least 10 other rabbits successfully spayed and neutered without any problems.
My other rabbit that died, I feel that he may have been able to be resuscitated if he had been more closely monitored(which would likely have happened at a more experienced rabbit clinic), but I'm just guessing and don't really know if he could actually have been saved. Because he was a young rabbit, I didn't have any bloodwork done, which if I had may have shown the vet there was an underlying health problem.
From my experience, having bloodwork done and having an experienced rabbit vet do the surgery where they also intubate the rabbit, is something I would insist on now. It is more expensive but it could be the difference of a rabbit successfully making it though the surgery. It certainly made a difference for my second bun. He had bloodwork done that came back normal, and the only difference with the second successful neuter surgery, was that the second vet intubated him.