The answer to your question is a very sad story. Momaday's own grandmother, Aho, witnessed the last Sun Dance. The answer can be found in the final part of The Way to Rainy Mountain entitled "The Closing In" that accurately depicts the decline of the Kiowa tribe.
Aho, Momaday's grandmother, actually participated in the last full Sun Dance (that included the completed religious rituals) as well as the very last Sun Dance (that left the rituals incomplete). Aho participated in the last full Sun Dance in 1887. The Sun Dance always took place along the Washita River and Rainy Mountain Creek. When Aho was ten years old, she witnessed the very last Sun Dance which, sadly, was left incomplete. Why was it left with the religious rituals undone? The reason is simple and can be summed up in three words: Fort Sill soldiers.
Under orders from the United States government, soldiers from Fort Sill showed up on July 20, 1890. This was right in the middle of the Sun Dance. At this point, the Fort Sill soldiers, due to their advanced weaponry and numbers, stopped all the proceedings of the Sun Dance and dispersed the Kiowa tribe. It is July 20, 1890 that is the date of the Kiowa tribe's surrender.