My skin was great a few weeks after birth until a few months after I stopped nursing my son. He was about 11 months old when I officially stopped nursing. Shortly after that, the acne came back. My mother, who had five kids, swears her acne was terrible as a teen and was much better after she had her first baby.
Birth control pills never helped my skin remain clear, though, and spironolactone never helped, either, so I'm not sure what it was about the nursing that helped my skin.