The best explanation for why the Missouri Compromise of 1820 did not have lasting effects is: The compromise only applied to the lands of the Louisiana Purchase, and a later law effectively overturned it.
The Missouri Compromise was primarily a response to the admission of Missouri as a slave state and involved establishing a line that determined the status of slavery in certain territories. However, it was ultimately rendered ineffective by later legislation, particularly the Kansas-Nebraska Act of 1854, which introduced the concept of popular sovereignty and allowed new territories to decide the issue of slavery for themselves, thus undermining the compromises made in 1820.