Why was slavery able to survive challenges to its existence prior to the civil war?

The Union was roughly divided into slave states and free states, and there were strong differences between the two parts of the United States; delicate political-legal balances were struck in Congress. Slavery supporters had large influence at the federal and local levels. And equally important, slave labor force was the basis of the South's economy until the Civil War.

So, keeping slavery was the deep interest of economic and political elites in the South. The Southern economy was mainly agricultural and could not have prospered and continued without large-scale slavery of black people.