Why did the north begin to lose interest in the southern reconstruction by the early 1870s

The North began losing interest in reconstruction in the South because the programs they were trying to use were not helping African-Americans as much as they hoped.

Northern politicians came up with the idea of the Freedmen's Bureau. This federal program would help newly freed slaves with housing, obtaining food, and other resources. Even with this help, African-Americans still struggled as Southern politicians continued to find legal loopholes to stop them from voting and obtaining equality. Along with this, the rising power of the Ku Klux Klan also made the job of reconstructing the South difficult as this group terrorized African-American citizens.

Their solution was to tax the colonists. 

Ithink it is called reservation