How can a woman become sterile after having a child before?

MANY reasons. Female fertility is dependent on a fully functioning 'female' system. Hormone changes may cause lack of periods & no ovulation (e.g. Pcos, early menopause). Also any obstruction of the fallopian tubes may cause sterility (usual cause= untreated std's e.g. Chlamydia). Fibroid tumors may develop and hinder implantation. A woman may develop sperm anti-bodies (yes, it's possible). Other causes, too.