I am aware of one soldier who had been granted a furlough, but apparently decided to remain with his comrades because a battle was imminent (Gettysburg): "I saw a dead officer lying with his pockets turned out. There were two papers on the ground lying close by him, one a furlough which was to have commenced two days before the battle and which was granted to allow him to go home and get married, and the other from his bride-to-be, expressing her happiness on the approaching event. The man was from New York, seemed to be about twenty-five years old and was a tall, well-made blonde ... his left arm had been torn from the socket, and he had bled to death." (John Cabell Early, A Southern Boy's Experience at Gettysburg, Journal of the Military Service Institution of the United States, New York: Governor's Island, 1911, volume 48 (May 1911), p. 419)
Another story involves the random drawing of a furlough while in winter quarters, which sounds a lot like playing the lottery: "In November 1863, one furlough was drawn by a 'woe-be-gone' soldier, who then sold it to a comrade named Jim for $1,000. Jim was a slick poker player and he had the cash." (A Private in Gray, Thomas Benton Reed, Company A, 9th Louisiana) (A nice sum for a private who earned $11 a month.)
I also recall that a Confederate soldier could obtain a furlough if he captured a set of enemy colors, which seems an effective if rather heartless method of encouraging men to take excessive risks during a battle. What irony to literally die for a chance to see loved ones again.