The point in which Montag would need to run would be in the final part of the book. It is at this point in which Montag has recognized "the truth." Montag understands his own condition and one that is no longer welcome in the world of burning books. Montag has recognized that he needs to break apart from such a setting. Running becomes a physical and symbolic act.
From a symbolic point of view, Montag recognizes that he needs to run. He needs to flee as far away from his world as possible. His relationship with Mildred is broken and he no longer is blind to the implications of his job. Physically, Montag is unable to run as fast as he would like because of his confrontation with the mechanical hound. As Montag fights with the hound, he absorbs a shot of anesthesia, which numbs one of his legs. The result makes it difficult for him to run: "He was afraid to get up, afraid he might not be able to gain his feet at all, with an anaesthetized leg. A numbness in a numbness hollowed into a numbness...." Montag's numbness is what makes him temporarily unable to run. The physical pain is what prevented Montag from running: "He stood and he had only one leg. The other was like a chunk of burnt pine-log he was carrying along as a penance for some obscure sin. When he put his weight on it, a shower of silver needles gushed up the length of the calf and went off in the knee. He wept." This condition is what makes Montag unable to run temporarily.
As the authorities pursuing him move closer on their "running feet," Montag wills himself to the condition of running. It is a slow and agonizing condition, but one in which he gains the strength to run after a certain point: "Now, sucking all the night into his open mouth, and blowing it out pale, with all the blackness left heavily inside himself, he set out in a steady jogging pace." This pace of running is established because Montag recognizes the urgency of the moment and the mental need to flee. It is at this moment where the symbolic action of running is matched with its physical action, facilitating escape.