Nephi saw that the righteous people who hearkened to the words of the prophet would not be destroyed. The "Son of righteousness" would appear to them, heal them, and they would have peace for three generations. This is exactly what happened in 3 Nephi 17 with the healing of the people at the time of Christ, followed by peace for three generations in 4 Nephi.
Have you thought about the impact your direct influence has over three or four generations? What is significant about three or four generations? You, through your grandchildren, are included in this span of time. Consider this: If you had been among those who had witnessed the teachings of Christ and if you had seen and felt his marvelous love, you could live to tell your children, your grandchildren, and perhaps your greatgrandchildren, about that remarkable experience. The period of three subsequent generations marks the affect we can have personally on others. Our direct influence does not reach through seven or eight generations because we aren’t around to personally know that later progeny.
The little children who were present and who personally interacted with Christ would have remembered that experience all of their lives. They were eye witnesses of the Savior and, throughout their lives, they could relate their experience to others. Therefore, for three or four generations, people who were actually there at Christ’s appearance—who were first-hand witnesses—were around to relate their personal accounts. However, after three or four generations, the opportunity for first-hand oral testimony would become lost, and people would have begun to ignore and discount the significance of what had happened. The people in 4 Nephi eventually went a different way and, when that happens, they were ripe for destruction. A century ago, a similar challenge was faced, when a generation arose that had not known Joseph Smith personally. Fortunately, intense historical efforts were made to record their recollections and experiences with the Prophet. This explains why the Church is so avid about keeping faithful historical records, and why our own personal histories should not go missing.
Book of Mormon Central, "Why Did the Peace Last So Long in 4 Nephi? (4 Nephi 1:16)," KnoWhy 225 (November 7, 2016).