Recently, I've started reading about the US Civil war and the events that led up to it. The primary issue was slavery in newly admitted states. The South didn't want more free states joining the Union because they were afraid of losing their superiority (or, atleast, balance) in the Senate. This, they were afraid, would lead to federal laws banning slavery in existing states too.
From what I've read, to forestall this concern, and to prevent possible secession, a lot of northern leaders (including Lincoln) proposed a constitutional amendment immunising slavery in existing states from being banned, but the South didn't accept.
Why was this? Were they afraid that if they let free states join the Union en masse, it would lead to more than 3/4th of the Union being comprised of such states, thereby rendering any constitutional amendment easily repealable? Or were there other reasons?
The amendment you are thinking of is the Corwin Amendment, which was passed in the waning days of the 36th Congress.
There were more than 50 resolutions proposed during 1860 to somehow protect slavery in hopes of saving the union from secession.
The Corwin amendment was passed out with razor-thin 2/3rds majorities in both houses.
It’s text was as follows, and it never directly mentioned Slavery though it was crafted to protect the institution:
“No amendment shall be made to the Constitution which will authorize or give to Congress the power to abolish or to interfere, within any State, with the domestic institutions thereof, including that of persons held to labor or service by the laws of said State.”
The south did not consider it a strong enough concession. Abolitionists in the north despised it.
Lincoln even sent copies of it to governors of southern states.
See:
MacVeagh, Ewen Cameron, “The Other Rejected Amendments,” The North American Review, Vol. 222, No. 829 (Dec., 1925 - Feb., 1926), pp. 274-283
Crofts, Daniel W. “Lincoln and the Politics of Slavery: The Other Thirteenth Amendment and the Struggle to Save the Union,” Univ. of North Carolina Press, 2016, pp. 125-142
The Wikipedia Article, “Corwin Amendment,” draws heavily on the Crofts work above, as well as others, and is actually quite good as historical Wikipedia articles go, so I recommend it for a quick overview before you get in to the major academic works.
It does sound like a good compromise on the surface, but there was a simple reason why it wasn't tolerable to the southern states. Before the civil war, the southern states held a pretty substantial amount of power in the federal government. Had they accepted this compromise, all of the territories would have become free states. It would have diluted the political power of the South and made it difficult to implement policies that benefited them. A union with an increasing number of free states but a stagnant number of slave states could force its will on the South. They wouldn't have to repeal the amendment. They could just pass laws that made slave holding increasingly difficult or less profitable. It would have left the South as a minority with very little power to influence policy. Accepting this compromise really wasn't in the South's best interests.