Why do Siamese cats get sick easily?

My piano teacher owns five or six (indoor) Siamese cats. They are very well taken care of; however, they seem to get sick really easily. One of them recently died of a mutated version of peritonitis and was only three-years-old. I've also known other people with purebred cats and those cats get sick easily. Me and my husband only have owned mixed breed cats. Our current set are over six years old and they have had no major health problems whatsoever. Is the reason that purebred cats more sick is because there is inbreeding at the "catteries"?