Are there reasons the villain would spare the hero, besides being threatened by him? As a writer, I'm just trying to find this out.?

1. Both are too injured to kill each other
2. The villain doesn't want to kill people
3. They are siblings and "Mother wouldn't want me to kill you."
4. Someone they love intervenes
5. Random/important person intervenes
6. Cops/FBI/etc comes
7. Does the movie cliche where the villain does his "tell the hero everything" speech but just as he's about to kill the hero, the hero gets saved.
8. Assumes hero's already dead
9. Hero escapes
10. Some magical curse doesn't allow the villain to kill the hero
11. The hero is really someone else in disguise
12. Torture to get info from hero
13. For money/prison
14. To frame hero
15. The villain isn't what he appears to be
16. Villian is really the good guy
17. You just end the story there for a good cliffhanger for the next book/story/chapter.

Then again we shouldn't be giving you these, it's your book and you are the author so you should be the one figuring out so and so. It also depends on the villain, what are his motives, what's his personality and connection with the hero? It's up to you to figure it out.

He needs someone to take the fall.

There are many possibilities. Your villian could have been being manipulated in some fashion so tries to avoid killing the hero. Nothing says the villain can't have a change of heart either maybe falling in love with the hero and saving the world together. It's really all about how you build up the villain. Are they just trying to get revenge, do they not know the whole story? Are they human and make mistakes and then want to repent. The villain can be and do whatever you want them to. Don't be trap by the normal villain hates hero tries to kill hero and hero wins setup. There are millions of other possibilities.

Who is threatening whom? Your question has the villain as the object of the hero's threat. That's weird if the villain has the choice of killing or sparing the hero. The hero might threaten, but if he does not have the power to carry out the threat, why bother wasting breath on threats?

The other people who answered you question gave you what I would have said.

1) ransom
2) coerce to act for the villain
3) preserve to torture, either mentally or physically or both
4) hero is dying of natural causes anyway (whether true or misunderstanding)
5) inconvenient now wait for a better time
6) just leave hero incapacitated, forest fire/wolves/neighborhood serial killer will get him

Yes. I have forgotten most of this but there was a specific tradition, in ancient Arabic times whereby a man overcome by attackers could request, of the victor "God's Mercy" or something similar. Arabic folk tales involve stories where the colleagues of the robber who has agreed to this form of 'sanctuary' wish to kill the victim, but are advised by his adversary that in accordance with religious law, he must kill them, rather than allow them to kill his captive. Can't remember the particular text. Will try and find it.

Yes, to keep the storyline going and make the sequel very interesting. Many films have the stories of the hero intertwined with the villain and sometimes only reveal this late, during important moments which keep everyone on edge of their seats!

Lots of reasons. Some examples (there are a zillion more)
- the villain only kills certain types of people, and the hero does not fit in that category
- the villain is related to the hero and won't kill a member of his own family
- the hero is a fellow of the villain (fellow countryman, fellow mason, fellow Christian, fellow Illuminati, whatever) and the villains moral principles prevent him from killing the hero
- the hero is weakened / defenseless / ill / or for any reason at less than peak performance and the villain considers it dishonorable to battle (and kill) someone in that condition
- the villain believes himself to be so much more powerful than the hero that he considers it not worth the trouble to kill the hero
- the villain wants the hero to "squirm", to suffer, and so he lets the hero live so that the hero can witness the villain's villainous success

etc ad nauseum

Without the hero the villain wouldn't be availing anymore nobody would be after him it's like Helsinki syndrome you become dependent on your torture For company. Without cops there wouldn't be any Robers and without robbers there wouldn't be any cops. It's just a fact of life friend if somebody doesn't say not to do it. People won't chase after doing it! But let something become a crime and right away you have a crowd of people interested in doing it.

The obvious one is that villains take lives, and heroes may feel that's a moral wrong.