What is the ruling on the prayer of someone who performed ablution close to the time of the next prayer, then the adhan was called and she prayed, then found that discharge had occurred a short while after she finished praying?

What you mentioned about the necessity of performing ablution (wudu') for every prayer for a woman afflicted with vaginal discharge is correct. If you perform ablution and nothing exits from you before the time of the prayer expires, then your purification remains valid. If you pray the second prayer before anything exits from you, your prayer is valid and you are not required to repeat it. If you doubt the time of the discharge's exit, then it is attributed to the nearest time when its occurrence is probable. If its exit is probable after the prayer, then your prayer is judged as valid.