I have been currently reading about the Civil War and the Confederacy. In 1861, it was not an industrial power, but it was still the 4th richest nation in the world. It seems unlikely it could ever win an all-out conflict with the Union, but, in retrospect, had the Democrats come into power in the North or especially if Britain and France had intervened (they came rather close during the Trent Affair) the Confederacy could have survived. It certainly had the determination and massive nationalism to continue independently from the United States, assuming no further wars between the states broke out. Depending on this, the Confederacy would have prospered in all probability.
So I don't think it is so unreasonable for the Confederates to last into the twentieth century.