Escaping a kidnapping or other abusive situation
Evading an attacker (or attackers)
Getting away from a predator (human, animal, monster, etc.)
Avoiding harm in the aftermath of a disaster, such as a plane crash, avalanche, or bombing
Finding shelter to survive the elements

There are five basic human needs that, when missing from a character's life, could motivate them to pursue this goal. The following needs are all possibilities, but only one of them should be the primary driver for any given character. For more information on the relationship between human needs and outer motivations, please see this Character Motivation tutorial.

Safety and Security: When a dangerous situation presents itself and a child's safety is threatened, they will take steps to avoid it. But some dangers appear gradually, and the child doesn't realize their danger until they're full immersed in the situation (as in the case of an abusive relationship). They may then stay in that dangerous situation out of fear of rejection and what others think or due to self-doubt. Only when the situation escalates will they often be motivated to act.
Physiological Needs: This motivation is inherently tied to the character's physiological needs. When they feel that their very life is being threatened, they'll spring into action.