I have had 2 chinchillas die, both young. But I also have a pet-store chin who came to me pregnant and with a nutrition-related tooth spur who is 5 now and has not had a health problem since the spur. Of my girls who died young, 1 was her daughter, who had a congenital heart defect that gave out suddenly, probably caused by improper breeding (Inca was probably impregnated by her brother, and she wasn't from good stock anyway). The other got stressed on our cross-country drive, and developed stasis that I couldn't pull her out of despite force-feeding, drugs, and SQ fluids.
From what I've seen and experienced, many early deaths seem to be because of 1. poor genetics (some malo, heart issues), 2. poor care (often from misinformation, but sometimes from carelessness), or 3. GI complications to another, probably less fatal problem (infection, stress, etc). I don't think you can say that "cared for properly, a chin should live to be 15" because there will always be uncontrollable factors. But there are 2 major causes of death we can try to avoid - genetics, and poor care. And we can do our best to be prepared and informed so we can try to alleviate some of the GI problems that are so fatal.