Why, after 1850, was another "compromise" between the North and South no longer possible?
There are two major reasons for this.
After 1857, compromise was no longer possible because the Supreme Court had forbidden it. The ruling in the Dred Scottcase had said that Congress had no right to legislate on the issue of slavery in the territories. This meant no further compromises like the Missouri Compromise and the Compromise of 1850 (both on the issue of slavery in the territories) could be made.
The other major reason is that the North and South were coming to distrust one another more and more by this time. The Fugitive Slave Act in the Compromise of 1850 had deepened this distrust. As the 1850s went on, events made the distrust even worse. The most important of these events was the conflict in "Bleeding Kansas." This event and others made it so that there was little desire to compromise even in the time before 1857 when it was still legally possible.