There are a few factors that account for the change in the relationship between Jem and Scout. As they get older, they slide into more adult roles of male and female. Since Maycomb is a town where race and gender roles are quite clearly marked, roles which sustain a tradition that comes with racist and stereotypical practices byt the way, the older Scout and Jem get the more they are likely to fall into these roles. Thankfully, Atticus teaches them that roles can serve a purpose but such notions should be abandoned if they are used to sustain a culture of racism or exclusion. Young as they are, the children do not change their relationship because of Maycomb's class system; it just bears mentioning here.
The main reason the relationship changes is because Jem is a bit older than Scout and he's going through all the identity issues of an adolescent. It's also quite clear that he embraces growing up and Scout does not. Scout feels pressured into becoming a lady and feels awkward wearing a dress during Aunt Alexandra's missionary meeting. But Jem struggles forward to his teenage years. In Part Two, which begins with Chapter 12, Scout notes Jem's changes:
Overnight, it seemed, Jem had acquired an alien set of values and was trying to impose them on me: several times he went so far as to tell me what to do. After one altercation when Jem hollered, “It’s time you started bein‘ a girl and acting right!” I burst into tears and fled to Calpurnia.
Although Scout is quite curious and intelligent, Jem, being the older sibling, understands things a bit better. When Tom Robinson is convicted, it is Jem who is more upset because he's beginning to see the hypocrisy of the adult world.
Another reason the relationship changes is that their routines change. In Chapter 26, Jem enters seventh grade and is in the high school. He also goes out for football and doesn't get home until late. When they were younger, Scout and Jem simply spent a lot more time together. At the end of the chapter, noticing Jem became upset at the mere mention of the courthouse and trial, Scout went to Atticus for advice.
Atticus said that Jem was trying hard to forget something, but what he was really doing was storing it away for a while, until enough time passed. Then he would be able to think about it and sort things out. When he was able to think about it, Jem would be himself again.
This is Atticus' way of telling Scout about growing up. Going through adolescence, Jem is still the boy Scout grew up with but he's attempting to fit in. High school is like Maycomb in a sense. There are expected roles, classes, and cliques already established and kids usually find it easier associate with one of these groups. Jem is no different except that, from Atticus' teaching, he has a subtle indication that these expectations to fit in, just as they exist in Maycomb, can be used for opposing reasons: to allow people in and to exclude others. This might not be in the front of Jem's mind but it bears mentioning again. More than anything else, Jem embraces adulthood and even though Scout is a sponge for knowledge, she withdraws from adulthood (well, lady-hood is more like it).