I agree with Lurchergirl, it depends on the rabbit. It depends on their breeding quality, some are prone to illness whilst some are lucky.
We've always used Mr johnsons supreme rabbit mix and had good health mostly. Althought its a mix, they ate all of it so got the balance of nutrients. Some ate lots of hay, some ate only bits, and 2 barely touched hay. They all had a variety of veg too, and i know most people dont like it but a few commercial treats (such as alfalfa slims and rabbit ravilos with a herb/veg filling). They've lived to normally 8-10, with one being 13.
The only health problems we had was one bun that got an absess at 8 years old, who later died as his gut didnt start. He also had conjunctivitus from about 7 years old, which we were given eye drops for but never completely got rid of it. We also had a female who through me not knowing about ovarian cancer and getting spayed, got cancer aged just under 7, had an op to remove it, then 7 months later it spread so she had to be pts.
My current older bun is 7, shes had back teeth problems since she was a few months old, needing to be done every 7 months. This could be due to bad breeding, or the fact she doesnt even touch hay! Also, since january she's been having a few random health problems, which we still dont know the cause for some!
Other than these, we've had a few baby buns die, 2 a few months ago from the same litter, from a virus, and 1 about 7 years ago, he was constipated, but still eating, vet said feed lots of veg, next day he pooed everywhere but was found dead.
I think its to do with a balanced diet, and quality of life, and partly luck! Things like viruses you cant predict or stop, so they could hit any bun at any time. Flystrike sometimes cant be prevented either. A variety of nutrients and a high fibre diet no matter what brand of food is the main key. As is giving the bun quality time for cuddles, and time and space to run, along with things to keep the mind active such as toys, ramp etc.
My buns have always been kept in a shed/summerhouse, i dont know if this has anything to do with them living a bit longer, through less contact with rain, wind, bugs, foxes etc, the things that could bring on illness. I believe iv had a lot of luck with my buns, as we didnt know about thing such as vhd or mxyamatosis jabs so none, up until my new buns, have ever had it. We didnt know what veg was suitable years ago, so by pure luck gave them suitable ones. And swapping over diet, we just did suddenly up until the past few years, with no problems.