Any laying hen can have a reproductive problem. There tend to be a higher percentage of issues in breeds that are bred for prolific laying. Leghorns would be one of those breeds. I've heard them referred to as 'ultimate egg laying machines', and they are often used in commercial egg laying. Having said that, there are lots of heavy layers that can live to a ripe old age, and likewise, others that lay less that can still have a reproductive problem.
