My contention is that as a nation, the CSA would not have been likely to prosper. Consider:
- The nation was largely agrarian at the time of the industrial revolution
- A non-negligible portion of the basis--slavery--was on the verge of ending legally worldwide or had already been abolished when the nation was founded (in OTL, I believe only Brazil had institutionalized slavery later)
- Several of the economic underpinnings were becoming obsolete (naval stores, since wood sailing ships were in decline) or alternative sources could be had fairly easily (e.g., cotton from Egypt or perhaps India)
- While there might well have been coal in some abundances in parts of VA and TN, I don't believe there was much at all in the way of exploitable mineral resources (e.g., iron ore) elsewhere, but I could be wrong. That would decidedly hinder industrial development and tilt the balance of trade unfavorably. It gets worse when copper becomes of interest after electricity becomes practical.
So...my contention is that by the late 1880s / early 1890s, the CSA is an economic hinterland--an economic client state, if you will--to the USA. Almost anything of an industrial nature has to come from either the USA or from Great Britain, paid for by an increasingly overburdened agriculture. I'd guess that by 1895 an economic crisis would be looming, and there would be rumblings, especially in the more advanced (a relative term!) states like VA that the idea of independence was not so hot an idea after all--and the corollary of reunification with the USA would necessarily be part of that.
The straw that breaks the camel's back: in the late 1890s, Cuba, just 90 miles from the Florida Keys, is in upheaval. That might seem to be a prime place for CSA expansion, but with the bank account nearly empty and no navy to speak of, Richmond is powerless to do anything. And when Washington is able to send the
Maine from one of the well-outfitted Navy yards in, say, Philadelphia, Boston, or Brooklyn, the CSA can only grind its collective teeth in frustration that once again, the Yankees have trumped them.
That precipitates a crisis in Richmond; namely, if we can't even do anything about Cuba because we're so penurious, what does that say about our future? Tired of relative poverty, at least one of the states (guessing likely TN) severs its ties with the CSA and applies for readmission to the US. And then the dominoes start to topple, especially when the relatively well-to-do and well-educated upper economic classes of Richmond and New Orleans see where the future lies...