Myself, and a few people in horse discord, have noticed when we dump a bunch of male horses into the breeding market (viewable to self) and then try to breed them they become unaccessable. I've tried reloading (swapping to and from different characters - did not work), completely restarting the client (did not work), and then manually removing and returning all of the horses for breeding. Someone else in the horse discord suggested to add or just remove/readd one horse, which does fix the issue.