Slavery is just not going to become uneconomical. However you try to logic your way around it, the data says it's an extremely profitable and efficient economic institution; they're not going to 'realize free labor is more efficient' because it just isn't. Antebellum Virginia pointed the way; even if cotton suffers a contraction, they can made great profits off slave wheat and corn production, and were using slaves to build railroads, to mine, to work in sawmills and distilleries and iron works. By renting out slaves, they can mimic the economics of free labor; I can imagine lots of slaveowners not even putting their slaves to work for them, just renting them out into whatever sector of the economy gives the best returns on labor.
Slavery was often fairly profitable for those engaged in it, yes, that much is true. But it's also not at all true that free labor is no more efficient than slave labor; it was, in fact, rather more efficient, per capita, not just with agriculture, but other occupations as well.
And while slave renting might have become a thing, one would still have to deal with fair few problems with slave labor that would be far less common with paid workers, regardless, such as sabotage, intentionally shoddy work, etc.-indeed, even IOTL such incidences were not that rare, even in factories; objectively speaking, it can be easily argued that it's really quite surprising that it wasn't even more of a problem, considering what was happening on plantations, etc.
Furthermore, slavery would, in fact, have eventually become uneconomical, even if the C.S. state and federal governments continually intervened on the system's behalf-particularly where agriculture was concerned, technology would have made maintaining a large farm much easier, with tractors, etc.., becoming fairly common by the 1920s, maybe the 1930s at the latest(right around the same time they did IOTL; combine harvesters followed not much later than that, by about 1950 or so).
I have an idea for another scenario, what about a huge speculation bubble regarding slaves? I don't know if the CSA could survive that long, but imagine a time where the demand for slaves goes up, as well as the prizes, even lower middle class whites start buying one slave or the other, if only for speculation purposes, maybe even on credit and working extra hard to keep up with the payments. Wouldn't that be ironic?
It has happened with houses, so why not with slaves.
Eventually the bubble will burst, a lot of people will be bancrupt or deeply in debt.
The market for slaves could collapse, keeping slaves around just incase the market will recover is not as easy at it is with houses or stock...
So if you can't sell your slave, because nobody is buying, and you can barely feed your own family you'd no choice but to tell him or her to get the hell out.
Maybe some old planter families would keep slaves after that, but that would be an oddity...
This is a scenario that I myself have brought up on a number of occasions, and it makes perfect sense when you really think about it; it is, in fact, an inevitability once the timeline gets long enough.....which in a surviving C.S.A., it's very likely to get there, with the only real difference being how badly the bubble bursts at the end of it all.
Wrecked in the short term. In the long term, it was a blessing, for it forced the South to diversify its economy.
That much is very true. Unfortunately, however, the Confederate leadership would likely never come around to that fact unless it were forced upon them somehow; as @Sift Green rightly pointed out, slavery was pretty much already part of a whole way of life, much like Communism in the Soviet Union.