Keep asking, knocking, seeking
21 And Jesus went away from there and withdrew to the district of Tyre and Sidon. 22 And behold, a Canaanite woman from that region came out and was crying, “Have mercy on me, O Lord, Son of David; my daughter is severely oppressed by a demon.” 23 But he did not answer her a word. And his disciples came and begged him, saying, “Send her away, for she is crying out after us.” 24 He answered, “I was sent only to the lost sheep of the house of Israel.” 25 But she came and knelt before him, saying, “Lord, help me.” 26 And he answered, “It is not right to take the children’s bread and throw it to the dogs.” 27 She said, “Yes, Lord, yet even the dogs eat the crumbs that fall from their masters’ table.” 28 Then Jesus answered her, “O woman, great is your faith! Be it done for you as you desire.” And her daughter was healed instantly. 
This passage is one of the strangest in Scripture. Here you have everyone discouraging this poor woman, including Jesus, and in the end, she gets what she seeks. Why? What is the point of all of this? Why does Jesus discourage her at first?
I think that another passage in the Gospels, Luke 11:3-13, sheds some light on this:
5 And he said to them, “Which of you who has a friend will go to him at midnight and say to him, ‘Friend, lend me three loaves, 6 for a friend of mine has arrived on a journey, and I have nothing to set before him’; 7 and he will answer from within, ‘Do not bother me; the door is now shut, and my children are with me in bed. I cannot get up and give you anything’? 8 I tell you, though he will not get up and give him anything because he is his friend, yet because of his impudence  he will rise and give him whatever he needs. 9 And I tell you, ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you. 10 For everyone who asks receives, and the one who seeks finds, and to the one who knocks it will be opened. 11 What father among you, if his son asks for  a fish, will instead of a fish give him a serpent; 12 or if he asks for an egg, will give him a scorpion? 13 If you then, who are evil, know how to give good gifts to your children, how much more will the heavenly Father give the Holy Spirit to those who ask him!”
Is this story a physical representation of how we should continually seek Jesus?
The first thing this woman had to overcome was the resistance of those around her. She was opposed by the disciples, who just wanted to be left alone. She is even opposed by Jesus, who says “I was sent to the lost sheep of Israel”. However, she does not lose hope. Instead, she keeps asking. He refuses her twice. I know that when what I am praying for is not granted, I can be tempted easily lose heart and not continue. However, this woman persists, not willing to leave until she is physically dragged away from Jesus – as long as she is talking with him, she knows there is hope.
When Jesus asks her whether it is right to give the children’s bread to the dogs (referring to his giving her something which Israel has not fully received), she counters with the same analogy – that even the dogs get the table scraps. This amazes Jesus, who surely knows that this is how she will respond. Instead of discouragement, she looks for any opening in Christ’s words and takes them, no matter how small. At this, Jesus marvels at her faith and heals her daughter.
How often do we lose heart when praying? How often do we scour the Scriptures for promises that apply to our prayer needs? I know that I often just pray as if “well, God, if you want to do it, sure, go ahead.” However, I should not be content for this approach, but instead plead with God for mercy. I should be as active in prayer as she was in pleading with Jesus. If God appears to not answer, I should plead all the more, basing my appeals in God’s scriptural promises! How often are we content to simply leave well enough alone and not seek after God with a faith that can move mountains. We should ask (the Greek indicates a work that means keep asking), and it will be given to us. Our good God will give us what we ask for.
Let us be like the persistent neighbor and the Caananite woman – both would not leave until their needs were met.