http://www.nytimes.com/2014/10/17/upshot/black-turnout-in-1964-and-beyond.html This NY Times article indicates that African American election turnout dipped after 1964, and did not exceed 60% until 2008. What are some possible reasons for this decline from '68 onward?
One variable you're not taking into account is that voter turnout for all Americans was steadily going down during this period. Whereas the percentage of the voting-age population who participated in the 1960 election was 63.1%, by 1996 that number had fallen to 49.1%.
In point of fact, the gap between the participation of black and white voters has steadily been narrowing since the passage of the Voting Rights Act:
...the racial gap in voter registration in former Confederate states shrank from nearly 30 percentage points at the start of the 1960s to 8 points by the start of the next decade.
Turnout in the South saw a similar reversal. In 1956, voter turnout among blacks in once-Confederate states was roughly 50 percentage points lower than that for whites. That gap has narrowed since the Act was passed and Southern black turnout has been higher than white turnout in four of the 12 presidential elections since.