I'm not sure how much of a cliche it is in Civil War timelines, but certainly in many threads about the prospects of an independent CSA there are people claiming that the Union will never give up on trying to reconquer the CSA. I think its safe to say the Union will eventually give up on putting the cat back in the bag, refocus on influencing southern politics and economically dominating the south.
I consider it far more likely that the Confederacy would be revanchist. Based on the Confederacy's actions during the ACW, they appeared to believe all slaveholding states were rightfully theirs, plus a route to the Pacific. Unless they produce a general who makes Robert E Lee look like Leonidas Polk and can get along with Jefferson Davis, that isn't happening. The Confederacy would probably wouldn't even keep all of the 11 states that seceded; there's a good chance they'd lose West Virginia and part or all of Arkansas or Tennessee.