Hi and welcome to BYC! They don't necessarily stop laying completely, they just decline in production. Like my birds are 5 years old now and in the summer we get on average an egg a week from each bird. Breeds that are meant to be commercial layers will lay a lot when they're young and then burn out when they're older because that's what they're bred for--maximum production for a short period of time. So, if you're looking for longevity, some of the hardier breeds may lay with less problems for slightly longer, but there will still be a decline in production and possibly less eggs to start out with. Good luck!