It will go away in stages, with the Industrial Revolution being the biggest threat to slavery as we know it. Simply paying a wage, albeit a shitty one, is usually more cost-effective than housing and feeding a slave, not to mention the increased security costs. This means a lot of out-of-work blacks in the CSA along with a bunch of slave owners who suddenly have worthless slaves. The question is, how do they keep from losing value on their slaves?
Picture plantations turning into "factory plantations" - lots more machinery and lots more accidents, but a similar amount of security. Slaves will still have reduced value, but "slave liquidators" help plantation owners recoup some costs while helping others staff these massive plantations. White workers get the Industrial jobs while black slaves and freed workers end up with what's left.
There's one thing that could work in a few different directions here - unions. In the USA, if workers are unionized, thanks to favorable labor laws, owners have no choice but to play ball. In the CSA, if workers unionize, they have to stay below the threshold of "it's just cheaper to buy slaves to do the work" and things can only get so good for them. That's assuming that demand for workers doesn't exceed the number of workers available, in which case, we'll see slaves cutting deals for freedom and slavery becoming rare, if not unheard of or flat-out illegal.