A Confederate victory could have so many unpredictable effects on attitudes regarding social stratification, slavery, human rights, property rights, racism, and nationality (both in the CSA and USA) that the institution theoretically could survive until today.
My own belief is that the CSA fought the ACW primarily because they saw independence as the only way to preserve their right to own slaves after Lincoln's election. Slavery is a foundation stone of the CSA and it was enshrined in the CS Constitution. Even if the institution becomes economically less viable (which it would), it would likely survive at least into the early 20th century. I have a hard time imagining that it would be made illegal until virtually all of the leaders of the generation that fought in Civil War passed away. Slavery probably would fade away as an actual practice, but stay legal long after the economic justifications for it no longer applied. I see this as equivalent to modern US use of the death penalty (it is still legal on the federal level and in most states, but its actual application in many states is becoming virtually nonexistant).
I would also hate to be a "freed" black person in the CSA because I think it's a near certainty blacks would be treated far worse than blacks in South Africa under Apartheid. No citizenship, no political rights, second-class legal protection at best, no opportunity for all but the lowest level of education, and probably not welcomed with open arms if they attempt to immigrate to other nations such as the USA.