The late L. Stromberg, of Stromberg's Hatchery, and founder of the national poultry museum, reported the case of a 28 year old hen who apparently occasionally laid an egg.
Any high producing hen is prone to reproductive problems. Much of what is sold as "Heritage Stock" is actually show stock, long removed from being bred for any utility value. Some breeds became "Heritage" as a result of breeding for show points to the detriment of utility value. (For entertainment, there are pictures of Queen Victoria's original Cochins, a bird with essentially clean legs and an upright, lean stance. Within a few decades breeding for feathers had made them too slow fattening for meat use, and had reduced egg production to a trickle.)
The first death in my 2011 flock was a Barred Rock who succumbed to fatty liver syndrome; the second was the Black Star who died of adenocarcinoma. The other Barred Rock is living happily, and laying regularly in a new home; while the remaining Black Star stopped laying during her last molt and doesn't seem to have resumed. The Dominiques lay about every other day, or a little more. It will be interesting to see how their health holds up.
Bantams seem to be the most long lived.