The best explanation for why the Missouri Compromise of 1820 did not have lasting effects is: The compromise relied on popular sovereignty, and public opinion was overwhelmingly opposed to it.
While it is true that the Missouri Compromise applied only to the Louisiana Purchase territory and was later effectively challenged by laws such as the Kansas-Nebraska Act, the fundamental issue was that it attempted to address the contentious issue of slavery through compromises that did not resolve the deep-seated divisions in public opinion. This ultimately led to further conflict and the eventual breakdown of such compromises in the years to come.