should it survive it would eventually end slavery just due to its attempt to survive in the world. It will be difficult when people turn from simply not caring to issuing embargoes, etc. to not do so. So, how late is open to preference, no matter how misguided it may be, but all states would eventually get rid of it, and this would be well before 1920.
Now, how long it would last depends on how the US fares without the southern states, as they do have their major perks. As also affecting this situation is any other states (Utah, etc.) that may get ideas in the event that the South is successful in their ventures. So, it is important to view how the world reacts outside, to judge the inside in this CSA.
Secondly, it heavily depends on leadership. If they have a string of Jefferson Davis's, they'll be gone by 1920. If we have a string of very strong leaders.... it could last a lot longer.
simply saying it would crumble quickly, "cause slavery" is not only short sided, it is not a very good assessment. In short, its hard to tell as well..... it's all guess work to what would occur. But..... most would just like to say roughly 30 years.... But I tend to think in a longer perspective.