First, remember there was no one "South", but at least three quite different "Souths":
But in the Upper South slavery was powerfully entrenched in the majority or regions, and controlled their governments.
The map below will explain much.
Absent Civil War, how long might that have continued?
Well, what would have stopped it? Nothing I can think of.
Oh, people say, but mechanization would have eliminated the need for slaves.
No, no, no, FRiends, mechanization would have eliminated the need for poor white trash, not slaves!
Even by 1860 slaves had well demonstrated they could both operate and help build any contraptions that white engineers might devise.
So slaves would always be needed, because slaves worked!
It was useless white people who would have no place in the future's "brave new world".
Of course, historically now things turned out quite different, with huge numbers of all races living off the government dole... but your question was slavery's potential future, and so that's your answer, FRiend.
The Cotton Kingdom in 1860, total production was 4 million bales worth $191 million, a huge sum for the time:
Thanks Joe. Very informative.
Mechanization: You totally dissed this one, saying that blacks would be needed to operate the machinery. Perhaps, but a plantation that once required 100 slaves would now only need 10. Mechanization on its own would at least cause slavery to shrink.
Popular feeling and opinion: The majority of people worldwide did not approve of slavery. The majority of Southerners were for gradual abolition. Did you know that there used to be more abolitionist societies in the South than in the North? That was before Northern abolitionists made themselves obnoxious by referring to the south by all sorts of foul names and calling the union with the south a compact with the Devil. It can be argued that the vitriol coming out of the North actually delayed slavery's demise by causing Southerners to take offense and stick by their guns on something they wouldn't have otherwise fought over.
Even so, the South would likely have abolished it around the time that Brazil did. If the South had won the war, Lee (among others) would have been a very prominent, respected, and persuasive voice urging for emancipation.