They will keep producing their whole life. However, production drops way off after 3 years. My wife isn't keen on butchering or I would make soup with old hens. I have some freeloading birds right now that will get to live out their life while only giving me manure and an occasional egg. When they die they become compost.

I do keep dual purpose birds in the event that food supplies require a sacrifice to feed my family. It costs a little more to feed heavier hens but the security is worth it.