There is a risk with ANY animal (and with humans) that they could die while under. But, it should be a LOW (1% or lower) risk. With rabbits, you need what they call an exotics vet. Vets do not get trained in rabbits, hamsters, ferrets, reptiles, birds etc in normal vet school. If they want to take the classes having to do with those animals, they have to pay for special classes. They also have to go to special seminars and such to keep up to date with their care throughout their career. So, a regular dog/cat vet, no matter how awesome they are, cannot treat a bunny – even though many of them will insist that they “treat rabbits all the time” and then make mistakes with our beloved pets because they won’t just admit “I didn’t study that particular animal, let me give you a reference for someone I know who does work with them” – I have no idea WHY vets don’t just say that.
I called around to a bunch of vets in my area and they all insisted they could treat rabbits and then when I quizzed them on bunnies, they didn’t have a clue. They wanted to fast them before surgery (rabbits cannot vomit, so they can and should eat right up to surgery time and my vet let me put some hay in the carrier so they could munch on it until surgery time and then if they wanted to after) which is dangerous since GI stasis is a problem and bunnies don’t like to eat right after surgery, so starving them for a day before that as well is just adding to the risk. And they didn’t even know what antibiotics were toxic to rabbits. Dog/cat vets have assured owners they know how to care for rabbits and then given them frontline, which is fatal to them.
So, if your vet is just saying “there is a risk, we let everyone know this with any animal” that’s normal and while it’s scary to hear, it is a possibility and they should let you know that. However, if your vet was saying “this is a really risky procedure with rabbits specifically” … find a new vet. And do not be afraid to ask to speak to the vet directly when you call around and ask them a few basic questions – what flea medication is good for bunnies, if they should fast before surgery, etc. If they cannot answer those, they have no business touching your baby.
Edit: Some vets like to do blood work and an exam before surgery, to make sure the bunny is in optimal health and has the least risk of complications. While calling around, if the price seems high at some place, be sure to ask what is included. Blood work will run a little higher and an exotics vet is typically a little more expensive than a regular dog/cat vet.