So, somehow even with their single cannon factory, no proper industry and massive population disadvantage the south 'win' the war, probably in terms of either keeping all or most of the territory that left the union. Maybe the union soldiers all choked on cotton or whatever...
Anyway, how long does slavery persist? For the last 800 years at least some cultures have not bothered with slavery because it isn't as good an economic model as having rent paying serfs or consumers as employees. Would they be able to keep their agricultural model profitable into the twentieth century? Would moral questions intervene? Or would it only persist for the minimum time it took what was left of the USA to get its act together and reinvade?