The south had a high level of food production. why would it have been difficult to maintain this level during the war, let alone increase it?

It would have been difficult to maintain the level of Southern food production during the Civil War, let alone increase it, because the South relied on a slave labor system against an opponent that was actively fighting for the freedom of slaves. As enslaved peoples rarely enjoy being enslaved, many in the South fled to Union lines as they approached which continuously weakened the productive capabilities of the South.

Population growth is one way