Cockatiels have the potential to live into their 20's or even their 30's so "old age" can't exactly be blamed....
However, birds fed a poor diet their entire lives do tend to age faster than birds fed a healthier diet.. that is, they are more prone to health issues than birds who are well cared for.
My own cockatiel is 17 and still lively as ever. Lost one cockatiel last year that was 19+ years old. Unfortunately, I don't know exactly how old he was, but I'm sure he was probably at least in his 20's. I feel like another tiel I lost was also probably in her twenties, although I'll never know for sure... what I do know is that she was at least in her teens.
Never easy losing a pet, regardless of how long you've had them. As has been stated though, without a necropsy, there's no easy way to even guess what might have gone wrong, and it might not have had anything to do with you... or maybe it did? Either way, I wouldn't recommend a necropsy now.
Actually Monica, while Cockatiels can potentially live into their 20's (into their 30's is extremely rare), unfortunately the average lifespan for a Cockatiel in captivity is between 15-20 years, and that could be under the best of care by their owner. My mother bred and raised Cockatiels for over 20 years, and her "pet" Cockatiels, not her breeders, lived in a massive, indoor aviary, were fully-flighted and got to fly every single day of their lives, and were bred and hand-raised/hand-fed by her and weaned directly onto the best diet a captive bird could eat...and they got more attention and love than I did as a child, lol. While I got really into owning and breeding/hand-raising English and American/Australian Budgies, my mom was all about the Cockatiels (she also has an CAG which she got from a friend of her's who was a breeder when he was just weaned, and he's now 32, so she just loves these guys). She had 5 "pet" Cockatiels that were never bred, not once, 3 of them were siblings, all males, and the other 2 were siblings, one male and one female.
The one of the 5 that lived the longest was 23 years old when he died, and the female lived the shortest amount of time, passing away at 18 years old. And knowing a lot of the people who bought hand-raised baby Cockatiels from my mom, the record for the well over 100 that she bred/hand-raised and sold as far as their life-span was 25 as far as she knows, and that's ancient. Also, my second-cousin and her husband opened a wonderful, privately-owned pet shop in my little, tiny hometown back in 1992 when I was 13 (it's still open and still owned by them but run by their son and his friend now). While they are both "bird-people" and they have a Blue and Gold Macaw that they bred and kept as their baby the year the store opened in 1992 and then later got a CAG, my cousin was the bird-breeder for the store. She bred and hand-raised every single bird that they sold in their store, everything from Canaries and Finches to Budgies and Cockatiels, to different species of Conures that weren't at all popular or even well-known by the general public back in the early 90's...and her husband bred and raised all of the reptiles/amphibians that they sold (still does in his home) and all of their freshwater and saltwater fish. She stopped breeding their birds for sale about 10 years ago, though he still breeds most of their reptiles, amphibians, and fish in their home...So now they only sell birds that they can buy locally from breeders that they know, mostly Budgies and Cockatiels (used to be from me) and occasionally some other birds...Anyway, we have had the discussion many times about the lifespan of certain species of birds, what can lengthen them, what can drastically shorten them, etc.
A hot-topic of conversation for myself, my mom, and my cousin (with me being a Budgie breeder/owner) is how most of the general public really, truly believes that the average lifespan of an American/Australian Budgie is around 5-7 years, when in-fact their average lifespan when they are fed a diet low in fat, as many Budgies die young of both Fatty Liver Disease and different fatty tumors that cause vascular and respiratory issues, is between 15-20 years old! My first Budgie lived to by 18 years old, just shy of 19, and the oldest that I've ever had was 21...So my question to my cousin and my mom was always why do Cockatiels not have a longer lifespan than Budgies, assuming they are fed a healthy, varied diet and not bred to death...If you asked either my mom or my cousin what the average lifespan of a Cockatiel is, they would most-likely tell you that #1) Males usually live longer than females, as female Cockatiels have an extremely stressful tendency to lay egg after egg and clutch after clutch, infertile or fertile, doesn't matter, and this is extremely hard on their bodies and is thought to drastically shorten their lifespans, and #2) The average lifespan for a Cockatiel in captivity, when fed a diet low in fat and that is varied, is about the same as that of an American Budgie, between 15-20 years. And if you do a search online, read most books on the subject, or just research the stories of past Cockatiel owners, you'll find that 15-20 years is actually higher than what most Cockatiel owners report.
And yes, of course there are exceptions, and any individual bird can far-outlive their expected lifespan...I think the American Budgie recorded to have lived the longest died at 29 years old, and I'm sure there are reports of Cockatiels living past 30, but that is certainly abnormal and rare. My mom's Cockatiels who lived past 20 years old had a really good quality of life, but you could certainly tell that they were elderly birds.
So the bottom-line is that it is quite possible that Liz's Cockatiel, believed to be between 15-20 years old, did in-fact simply die of natural causes...Now of course, when a bird, a dog, a human being gets to be "elderly" and we say that they "died of natural causes" or that they "died of old-age", there is always an actual "cause" of their death, usually it's something like a heart-attack, a stroke, cancer, etc. So it's possible that Liz's Cockatiel did in-fact have some underlying disease-process that finally ended it's life, or maybe it had a heart attack, etc., but the bottom-line is that if her Cockatiel was in-fact 15 years old or older, then he lived to be on the high-end of the lifespan for a captive-bred Cockatiel, and actually lived to be far older than most pet Cockatiels live to be...