Just research it. And common sense think about it based on the north and south economies. Slaves were not inexpensive. Machines could do more faster and parts could be replaced. People get old and weaker and sick and injured and still had to be taken care of. They were living investments that required sustenance and maintenance. Further the south economy was built on crops, what they often sold was raw product, not end goods. The mills, which were industrialized, were in the north. Industry was not in the south.
It was only a matter of time. At least what others have argued.
I have seen it argued that their economy was doomed because Europe developed other sources for Cotton. The problem with this thinking is that Europe developed these alternative sources of cotton precisely because there was a US Civil War, and it badly disrupted their normal source of Cotton which was the South.
In the absence of the Civil War, slave produced cotton might still have been a profitable system for another 40 years or so. The increased capitalization the South would realize from selling it's product directly to Europe and avoiding the high taxes and middle man fees it was paying through New York, would have allowed the South to invest in more and more diverse industries in their own communities.
The South used to have it's own ship building industry. Those boarded up factories could have commenced building ships again, and the South could have carried it's own cargo.
200 Million taken out of the New York economy and transferred to the Charleston or Norfolk economy would have massively increased the capital available for industrial development.
It's not so easy for me to see that the cotton economy was doomed in the short run. Perhaps in the long run it was, but in 40 more years, it is quite likely the South would have diversified as the wealthy look for alternatives in which to invest.