Even though America is supposed to be a great "melting pot," most people still identify with their heritage as well. Most large cities have pockets of various nationalities or ethnic backgrounds. It is a source of pride and connection within family and community. Perhaps American Indians are connecting to something essential to their identity in order to ground themselves in something traditional that could bring greater spiritual satisfaction to their lives.
A few years ago there was a New Year's Eve segment about people who had traveled to South America for a celebration with some indigenous tribe. This ceremony for the New Year was one that had been conducted for hundred of years and was simple and primitive, but some New Yorkers from Manhattan extoled its praises.
In concurrence with the above post, there is some element of escapism in the act of retracing roots or returning to ancient rites. Perhaps, the simplification of things is also a relief from the complicated modern life.
It is not unusual, among people of any ethnic group or religion, for people to return to past ways when their current situation is not to their liking. I would argue that this is why the resurgence you mention could be happening.
We can see this sort of change happening even among white Christians today. They feel that they are losing "their" country to nonbelievers and liberals. As a reaction, they turn even more to the religion of the "good old days." Native Americans would have even better reasons for making a similar change. For many of them, the modern world is not working well. They are isolated and have many economic problems and social problems (most notably alcoholism). They might feel that Christianity and other modern ways have not worked for them and that they, therefore, should return to the old ways.