I think that was also the case of why they were able to go Super Saiyan so easily, so if your parent is a Saiyan and the other parent is Human, and your Saiyan parent never went Super Saiyan, it won't be so easy for you.  That and considering a half-breed doesn't have the combat drive as much as a regular Saiyan has, it might hinder them to becoming Super Saiyans.