Trace the story of God throughout millennia, and you'll find examples over and over again where it seems like people talked God into changing His plan. Why would the creator of the universe and the architect of time itself change his course, for anyone?
Even though we will never quite grasp how or why God would respond to our prayers, it's probably worth our time to study the instances in which He changes course. What kind of person does it take to pray those kinds of prayers? What kind of prayers are compelling enough for God to change His mind?