The correct answer to this open question is the following.
I think the U.S. backed down on its enforcement of the Treaty once gold was discovered in the Black Hills because the United States federal government had already signed and formalized the Treaty of Laramie in 1868, in which the government recognized that region of Black Hills as a territory of the Sioux Native American Indian tribe.
Let's have in mind that although large gold deposits were found in 1875 in Deadwood Gulch, Black Hills territory and thousands of people went there to find fortune, the territory already belonged to the Lakotas and the Sioux.