Change comes slowly to people, I am not sure at all that the mindset of all slave owners was to give up their slaves. The reality though was that slaves were very expensive, not just to purchase but to support. Each thing that allowed a slave owner to save on labor was leading to less slaves being needed. Some owners were turning against slavery for moral reasons- it became more and more common to give slaves their freedom. I have read many accounts of people inheriting slaves, and choosing to give them their freedom. There are also many accounts of people freeing slaves in their will.
I do believe slavery would have died out on its own, but the time frame- that is up for debate. I don’t have any idea if morals or the need for less labor would have led to it ending fairly quickly or over a long time frame. I know if I were a slave I would certainly not want to wait for freedom.
There's a lot of confusion on this topic because, it turns out, both of the following were true:
Tammy8: "I do believe slavery would have died out on its own, but the time frame- that is up for debate.
I dont have any idea if morals or the need for less labor would..."
It's sometimes argued that slaves would be eventually replaced by machines, but that ignores the facts that slave prices went up & down according to cotton prices and if cotton became cheaper (because of machines), slave prices would adjust accordingly.
Also, by 1860 slaves could build, maintain and operate such machines as they had, no reason to think they couldn't continue to.
So, in an alternate-history where there was no Civil War or Confederates won it quickly, there's no reason to think slavery would ever necessarily become more of a burden than asset in the Deep South.