When I saw your subject, it made me realize that if I'm asking myself whether to cull a sheep for a particular reason, ideally I probably should. There are 2-3 sheep in my flock though, that will live out their lives on our farm, most likely, just because they are more like pets (and somehow it seems they are coincidently our least productive ewes!!!).
I plan on culling if a sheep makes a habit of having lambing problems. One time may be a fluke, but if it happens twice, I'll think strongly about culling. For example, I'm hoping a retained placenta won't be a problem ever again with one of my ewes who didn't clean by herself this year.
I wouldn't personally put a cap on their age, and instead I rely on my production records. By not having a stated age where I cull, I will keep older productive ewes in my flock so that I'm keeping track of which ewes produce late in life and which don't...something that may eventually be one of the questions to ask when deciding which ewe lambs to keep as replacements. Of course, I guess the negative side to this is that by letting them become non-productive before culling, I lose a little in keeping unproductive old ewes when other people would have already culled them if they automatically culled at a certain age despite production records.
I'm curious now. Do other people cull at a certain age, or do you only cull when an older sheep becomes unproductive, regardless of her age?