I thought you said it was going to continue indefinitely?
"Indefinitely" means of no determined interval. It does not mean forever.
The Corwin Amendment would have made it longer, because then 3/4ths of the states would be unable to vote to abolish it. With the Corwin Amendment passed, slavery would persist until the very last state decided to give it up voluntarily, and that would have certainly taken longer.
Even then, I don't think slavery would have persisted for more than another 80 years. I think the advent of mechanization would render slavery obsolete, and then the slave owners would be more susceptible to social pressure because the economic pressure encouraging to keep slavery would have waned.
But this is all academic, because the North did not invade the South to stamp out slavery.