The seeds that the plantains produce get spread all over the place and so all during the growing season newly dropped seeds are germinating and growing so we get new plants all the time. The corn gluten meal can help control germination of any seeds that overwintered but those that are seeded in later would need another application.
The best method of controlling that germination is to grow a good thick turf, mow high, recycle the clippings in place to help feed the grass growing there, water properly, and get the soil into a condition that will grow strong and healthy turf grass that will not allow "weeds" to grow. Tall and thick turf will shade the soil so any "weed" seeds there do not get the sumlight they most often need to germinate.

Thanks for the advice! We will try more corn gluten to prevent new seeds from germinating.