When seen with other examples of faith which Jesus commended, we can see that faith was very important in granting requests for healing or justice, whether addressed to him, or to God the Father in prayer. We might say that just as a simple trust and belief in the parents power and goodness lies behind a child's persistent asking, so Jesus expected faith to show itself in persistence. That is the kind of personal interaction with God that should make a difference. It is important to understand the difference between faithful persistence and manipulation. The analogy with the child asking a parent can break down at this point.
Children can be manipulative.
Christian prayer is distinguished from magic precisely at this point. It is never manipulative, always trusting. We must trust God to decide what is good. Attempting to use a magical formula is manipulation in which a result follows mechanically if one does it the right way. Prayer is never like that.