Could the US have remained half-slave
and half-free forever? Why or why not?

Yes if the civil war was lost or didn't happen.

here are some events that to cause increased conflict between the north and south

1) mexican cession- gaining modern day california, utah, arizona, and new mexico from mexico. caused southern and northern politicians to fight over whether or not there would be slavery in these newly acquired territories.

2) uncle tom's cabin- this famous book described the cruelty of slavery in the south during the antebellum period, causing more northerners to support abolition and southerners to resent the book as they felt it unfairly depicted southern society.

3) kansas- nebraska act- disagreements over whether or not kansas and nebraska would be free or slave states caused issues between northern and southern politicians in congress.

4) bleeding kansas- this fighting took place in kansas after congress allowed this territory to vote on whether or not they would have slavery. citizens were killed and buildings were destroyed during this fighting.