Why was Jem determined to retrieve his pants alone from the Radley yard in Chapter 6?

The reason that Jem returns to the Radley yard to retrieve his pants is because he does not want to disappoint his father. Jem is maturing into a morally upright individual like Atticus and is considerate of his father's feelings. Before Jem leaves to retrieve his pants, Scout begs him not to go. Jem then explains to Scout that Atticus has never spanked him before and he wants to keep it that way. Jem also realizes that he was wrong for sneaking into the Radley yard in the first place. When Scout says to Jem that she is going with him, Jem tells her "no" because she will make too much noise. Jem does not want Scout getting Nathan Radley's attention and also does not want to put her in harm's way. Jem chooses to go alone back to the Radley yard where he finds his pants mended and folded on top of the fence.

Why was Jem determined to retrieve his pants alone from the Radley yard in Chapter 6?

Jem is also becoming painfully of what is right and wrong.  Not only does he not want to be punished by Atticus, but he also wants to be able to preserve his pride.  Jem is ashamed of what he has done and doesn't want anyone else (other than Scout, who already knows) to realize what he has done.  He doesn't want his father, especially, to know that he has done something to be ashamed of.

At one point, Scout tries to persuade Jem not to retrieve the pants.  She states that he'll only receive a whipping, but Jem does not want to be punished in that way, since his father hasn't done it before.  Scout says that Atticus has just never caught Jem doing anything wrong.  Jem replies, "Maybe so, but--I wanta keep it that way, Scout.  We shouldn'a done that tonight, Scout."  Jem's attitude makes it clear that he is growing up.

Why was Jem determined to retrieve his pants alone from the Radley yard in Chapter 6?

To cover his missing pants, Jem (and the other children) had to lie. This put their relationship with Atticus in danger. The missing pants are also a piece of evidence; they prove beyond doubt that the kids went to the Radley house, and that they were trespassing, etc. On a simpler level, Jem has to go because he is afraid, and he wants to face his fears.

Why does Jem risk his safety to retrieve his pants from the Radley yard at night?

In chapter 6, Jem and the children raid the Radley yard at nighttime and almost get shot by Nathan when he hears them trespassing on his property. As the children are escaping, Jem is forced to remove his pants in order to crawl underneath the fence and escape. Later that night, Scout hears Jem get out of bed, and he tells her that he plans on returning to the Radley yard to retrieve his pants. Scout fears for her brother's safety and begs him to stay in bed. However, Jem refuses to listen to his sister's advice and explains his reasoning for retrieving his pants, telling Scout,

I—it’s like this, Scout . . . Atticus ain’t ever whipped me since I can remember. I wanta keep it that way (Lee, 57).

Essentially, Jem admires and respects Atticus and does not want to disappoint him. Jem is aware that when Nathan Radley discovers his pants, he will inform Atticus, who will be disappointed and chastise his son. Jem wishes to stay in his father's good graces and is desperately afraid of disappointing Atticus, which is why he risks his safety returning to the Radley yard to retrieve his pants.

Why is it important to Jem that he go back to get his pants before morning?

In Chapter 6 of To Kill a Mockingbird, Jem is determined to get his pants back because he does not want to get in any more trouble than he already is in. In the previous chapter, Atticus had instructed Jem and the other children not to go to the Radley house. Jem, along with Scout and Dill, ignore those instructions which lead to Jem losing his pants in the Radley's fence. When a gun sounds, the whole neighborhood gathers in front of the Radley house to gossip about the gunshot they all heard. Apparently, Nathan Radley shot his shotgun in the air to scare off an intruder.

When Atticus interrupts the gossip to ask Jem where his pants are, Jem and Dill hatch an elaborate lie to explain why Jem is not wearing pants. Jem knows that this lie will not hold up come morning when Nathan Radley will likely find Jem's pants, fingering him as the intruder. He is mostly afraid that being caught disobeying his father and then lying to him will greatly disappoint Atticus. We know that Jem holds his father in high regard and wants to live up to his expectations of him. Therefore, he feels it necessary to take the risk of returning for his pants in order to maintain his relationship with Atticus.

Why is it important to Jem that he go back to get his pants before morning?

You can find the answer to this in Chapter 6.  I would say that Jem wants to get his pants back because he does not want to disappoint his father and make his father think less of him.

Jem tells Scout that Atticus has not whipped him in a very long time.  He says that he wants to keep it that way.  It does not appear to me that he is really afraid of the pain of being whipped.  Instead, it seems that he is proud of the fact that he and his father sort of related to each other as adults.  He does not want his father to think of him as some kid who needs to be whipped.