Will not a expert on this topic (Not my area of study) I can suggest a few reasons as to why this appears to be the case.

Probably the most prominent reason would be an influx in people reporting themselves as mixed between Native American and Caucasian. This would be the case with censuses throughout the US as the fact that the population in general was expanding at a rapid pace as well. Another thing to consider is the fact that the stigma against Native Americans shifted. Culture and society as a whole without a doubt looked at Native Americans in a kinder light than in previous decades. More individuals left the reservations and moved into cities thus spreading out the numbers even more. I think another aspect which is somewhat its own point but also tacks on to the first point is that people viewed it as 'cool' to have native blood. Ask people born in this time period and I'm 100% sure you will get a straight answer if they have any Native blood. Even if it is 1/64 Cherokee people will still claim they have Native American blood. Basically society made it cool to be Native as a result increasing the number of recorded Native Americans.