I have not heard too reference to individual counties (or parts of counties) seceding from a state, but one in AL did -- Winston Co. -- during the Civil War. And Lincoln did not take exception to that secession, as I recall.
Oh, I agree that none did .. except for the northern counties of Virginia becoming West Virginia. And I'm not saying that there is not a certain amount of hypocrisy on the part of the Northern States. However, where does the right to "secede" end. If carried to its logical conclusion, there is no end, meaning that any county, township, city, or conglomeration of families could secede from whatever larger area grouping they belonged to, becoming "independent" countries.