The following review might be helpful. Female rabbits may not necessarily die of uterine cancer but it is highly prevalent nonetheless. Rabbit experts agree that neutering females also helps minimise aggression, particularly important in the confined environment of the average hutch. Most rabbit rescues in his country will recommend neutering females. Perhaps your vet has evidence to discredit this, I would be interested to hear it.
Uterine Cancer
Toft, J. D. 1992. Commonly observed spontaneous neoplasms in rabbits, rats, guinea pigs, hamsters, and gerbils. Semin. Avian Exotic Pet Med 1:80.
The Biology of the Laboratory Rabbit, 1994 edition.
Adenocarcinoma of the uterus is the most frequently encountered neoplasm of the rabbit. Ingalls (J. Natl. Cancer Inst. 33:799-806. 1964) showed that 11 of 12 rabbits developed uterine carcinoma. Because of the number of rabbits developing carcinoma many researchers looked into the possibility of estrogen being carcinogenic. There was quite a bit of conflicting data, and the authors draw this conclusion "Data is extremely difficult to interpret because of the naturally high incidence of adenocarcinoma of the uterus in untreated rabbits."
Later, "Notwithstanding heredity as a factor, the incidence of uterine carcinoma has been noted to exceed 50% in certain colonies of random bred females kept past 5-6 years."
Ann NY Acad. Sci. 75:535-542 Green, 1958.
Greene monitored a colony of rabbits over a long period of time (8-10 years). All rabbits dying from whatever causes were necropsied. 16.7% of 849 rabbits were found to have uterine adenocarcinoma. The average age of the colony was greater than 4 years, which is important, because most lab rabbits are under 24 months of age. The tumor incidence in Greene's colony was very closely linked to age. In rabbits dying between 2 and 3 years of age the incidence of cancer was 4.2%. In rabbits 5-6 years of age the incidence is 79.1%.
We don't know what the different causes of death were, but they are listed as "natural". The incidence of cancer in males and females is about the same in rabbits under two years of age, after that, the incidence in females dramatically increases over the males, primarily due to uterine cancer.
We found the article in TBLR because it was referenced in a journal that claimed that the incidence of cancer was somewhere between 1 and 4% in rabbits. That low figure was compiled from laboratory rabbits, most under 2 years of age. So, that figure agrees very well with Greene's findings. When one starts looking at older rabbits the data drastically changes. Most of the veterinarians we've talked with seem to believe that this is very genetically controlled. TBLR even lists breeds that are not susceptible to uterine cancer. While 80% may not be a figure for all rabbits, it was for that colony. Other colonies have had >50% incidence of cancer.