If the cat is a purely house cat, no outside exposure, they can live to a very old age (18-20) and be perfectly healthy the entire time -- without vet visits.
One of my cats, who passed a couple of years ago, was 17 and died in her sleep. I only took her to the vet once to get her spayed, and she was never sick a day in her life.
I worked in vet clinics for several years, and healthy animals can be exposed to possibly deadly illnesses simply by going for their well pet visits. I never take my pets in unless they actually are ill or injured... which is rare. (But I've been caring for animals my entire life, those with less experience should always rely on their veterinarians expertise.)