I think you're missing the concept. Genetic material has to be replicated in new reproductive cells. Eventually, there are going to be mutations and variances. In other words, things can go wrong in the replication process. It gets worse as time goes on. An older deer has a much better chance of having some anomally show up in the genetic material it's passing on than a younger deer in its prime.

The reason they put old studs out is that they are still capable of passing on ideal genetics for racing champs. They may not be capable of winning races, but that doesn't mean they can't sire a winner. The chance of passing on a defective set of genes gets increasingly greater, though, as the horse ages and its replication process, like all other bodily functions, breaks down.