There didn't need to be one as it would have been an economical fact. I live in a rural area. Mule teams plowed the fields for centuries where I live. I do not own a mule. I use a tractor. A mule is a liability. I would have to feed it. Give it shelter. Tend to it's health as the loss of it would be a severe hardship. The tractor I can park until needed and it's needs are few. Apply that concept to slavery. As sure as it was dying in the north and a liability to most all persons yes it was dying as well in the south. It would not have lasted past 1890-1900.
Looking back over 140 years and claiming economic fact is meaningless. Looking at the mindset of the men of the period, and their reasons for their rebellion, is not. There was not a single Southern leader I'm aware of who was not convinced in 1860 that their great grandchildren would be enjoying the benefits of slavery. That is why they chose to rebel to defend what they saw as threats to their institution. And which is why claims that slavery would have ended in 20 or 40 or 60 years is pure speculation without any basis in fact.