The basic political situation that brought Reconstruction to an end was that the Republicans and the Democrats came to a stalemate in the election of 1876. This led to a deal being made in which the Republican (Rutherford B. Hayes) was allowed to become president and the Democrats got the end of Reconstruction.
By 1876, the North had largely grown tired of Reconstruction. There were many other issues that seemed much more important to Northern voters. These voters did not typically care all that much about the rights of African Americans. Therefore, they did not see much reason to continue with Reconstruction if Reconstruction was only for the purpose of protecting the rights of African Americans.
By 1876, the Republicans had already been retreating from Reconstruction. The South had plenty of political power and it was strongly against Reconstruction. The Republicans were abandoning Reconstruction because it essentially was not worth the loss of political capital in their eyes. When the election of 1876 was deadlocked, it seemed to Republicans that it made more sense to abandon Reconstruction in return for winning the Presidency.