There are a few possibilities as to why Native American Ancestry does not show up in your DNA.
#1) If your most recent Native American ancestor was more than five generations ago, you may have inherited little or no DNA directly from them. The farther back in your history you look, the less likely you are to have inherited DNA directly from every single one of your ancestors. This means that you can be directly descended from a Native American without having any Native American DNA. While you mention that you should be half Native American Indian from your biological parents, the parent who may have been from an indigenous tribe could very well have only had some DNA reflecting that within them and then it was not passed down to you. It is also possible that one of your parents grew up with the Native American culture but may not have had a lot of Native American DNA.
#2) Throughout American history, people without a genetically Native American background have claimed Native American heritage for a variety of social reasons related to the shifting politics of race and indigeneity in the United States. As a result, many families without any genetically Native American ancestors have passed down stories about Native American ancestry.
#3 The reason you didn't get any results in Native American could be because family stories about Native American heritage are often myths. Unless you have documented evidence of a Native American ancestor, it's not always safe to assume it's true. Does it sound like your 2nd great grandmother was supposedly full blooded Native American? It's possible she was actually less than full-blooded too, which means you may not have inherited any of the NA markers from her.
#4 Additionally, many sample groups for the Native American category are small. This is because most full-blooded Natives of North America are generally unwilling to participate in DNA testing/sampling. So, it is possible to have Native American heritage and have it not show up in the ethnicity report, because the sample group isn't big enough.