Ponyboy actually runs away twice in the novel. The first time he runs away, his motivation is the fight that he has with his brother Darry. Ponyboy is with Johnny and they end up falling asleep so Ponyboy goes home extremely late, getting Darry so mad and worried that he yells at Ponyboy. In response to this, Ponyboy and Johnny “run away” to spend the night in the park.
The second time that he runs away follows this part. While in the park a group of Socs finds Pony and Johnny and one of the Socs tries to drown Ponyboy. Johnny saves him by killing the boy who is trying to drown him. They then run away to live in an old church in Windrixville because they are wanted by the police for the murder of a Soc.
The previous answer states that Ponyboy actually runs away twice during the book. That is correct. The first time that Ponyboy runs away is in chapter three. Earlier in the story, Ponyboy and Johnny are hanging out, and the two of them fall asleep as the hour gets later. By the time that Ponyboy wakes up and gets home, it is around two in the morning. Darry is worried sick about Ponyboy at this point. His worry turns to relief when Ponyboy finally comes home; however, the relief quickly turns to anger. Darry is angry at Ponyboy for making everybody worry so much.
"I reckon it never occurred to you that your brothers might be worrying their heads off and afraid to call the police because something like that could get you two thrown in a boys' home so quick it'd make your head spin. And you were asleep in the lot? Ponyboy, what on earth is the matter with you? Can't you use your head? You haven't even got a coat on."
Ponyboy is very apologetic, but Darry is so upset that he slaps Ponyboy. Darry immediately regrets his action, but the damage is done. Ponyboy bolts out of the house. He’s angry at Darry, scared, and humiliated all at the same time. Ponyboy goes and gets Johnny and announces that they are running away.
It was plain to me that Darry didn't want me around. And I wouldn't stay if he did. He wasn't ever going to hit me again.
"Johnny?" I called, and started when he rolled over and jumped up almost under my feet. "Come on, Johnny, we're running away."
The second time that Ponyboy and Johnny run away is shortly after and a bit more out of necessity than the previous instance. Ponyboy and Johnny are out together spending the night in the park when a group of Soc boys corners them. The Soc leader, Bob, attacks and thrusts Ponyboy’s head under the water of a nearby fountain. Johnny reacts to save Pony’s life, and Johnny stabs and kills Bob. The two boys know that they are now in a world of trouble, so they decide that running away and hiding out is the best plan of action.
Johnny looked around, slapping his pockets nervously. "We gotta get outa here. Get somewhere. Run away. The police'll be here soon." I was trembling, and it wasn't all from cold. But Johnny, except for the fact that his hands were twitching, looked as cool as Darry ever had. "We'll need money. And maybe a gun. And a plan."
Both boys are at a loss, uncertain exactly how to run away and hide out, so they find Dally. He helps get them out of town for a bit by hiding out in an old abandoned church.
"Hop the three-fifteen freight to Windrixville," Dally instructed. "There's an old abandoned church on top of Jay Mountain. There's a pump in back so don't worry about water. Buy a week's supply of food as soon as you get there--this morning, before the story gets out, and then don't so much as stick your noses out the door.”
I think that he sort of got fed up with the way that Darry had been treating him and he just kind of snapped because he couldn't take this way of life anymore.