Finally, in addition to international pressure (which would occur, but probably not in the way some envisage), we have to take into account how hard it would have been for the CSA to abolish slavery.
Article 1, Section 9 (4) of the CS Constitution states "No bill of attainder, ex post facto law, or law denying or impairing the right of property in negro slaves shall be passed."
and shall have the right of transit and sojourn in any State of this Confederacy, with their slaves and other property; and the right of property in said slaves shall not be thereby impaired".
The also added something similar to Section 2 (3) of Article IV (changes in red): No slave or other person held to service or labor in any State or Territory of the Confederate States, under the laws thereof, escaping or lawfully carried into another, shall, in consequence of any law or regulation therein, be discharged from such service or labor; but shall be delivered up on claim of the party to whom such slave belongs, or to whom such service or labor may be due.
So even if Virginia did make all of it's slaves free, anyone from Alabama who had a slave could go to Virginia with said slave and the slave would still be a slave.
It is because of all of this that the CSA is very unlikely to stay in one piece. It would likely face a civil war / revolution within two generations.
The moment one state abandons slavery all hell would break loose. Same thing goes for the moment Texas discovers its oil deposits (and particularly true if the Indian Territory and the Arziona Strip are also part of the US.