The term translated "kept asking" (NKJV) or "besought" (KJV) is in the imperfect tense in the Greek, implying continuous action. Her persistence is seen in her constant pleading with Him and is emphasized by the fact that she pleads continuously in spite of the various rebuffs she receives. Few people would have continued praying after the first few rebuffs, as most of us are prone to quit if we do not receive a swift answer.
Christ says, "Men always ought to pray and not lose heart" (Luke 18:1)—and this woman did not lose heart! She faces four rebuffs that required great persistence to overcome to obtain help for her daughter: deafness to her plea (Matthew 15:23), discouragement from the disciples (verse 23), demotion of her position (verse 26), and deficiency in her opportunities (Mark 7:28). Are these rebuffs any different in principle to the ones we experience in our prayers?
Even though it seems that Christ sometimes ignores us, He does not really, merely delaying His response to strengthen our faith and resolve. Answers can give great encouragement, but delay checks our sincerity and forces us to be more fervent, strengthening our faith. Christ's turning a deaf ear to the woman's prayer should encourage us in our prayers when they are not answered immediately. Even the most sincere and faithful prayers, as this woman's was, can be delayed by God. Because we give up so quickly, delay exposes many of us as having little faith, so Christ frequently tests our faith to improve its quality.
We can never allow ourselves to be satisfied with our faith because, as God knows, we need more faith if we are to do more for Him. He rewards persistent faith that includes a full assurance of hope. Faith overcomes obstacles, personal trials, and the world. The apostle John writes, "For whatever is born of God overcomes the world. And this is the victory that has overcome the world—our faith. Who is he who overcomes the world, but he who believes that Jesus is the Son of God?" (I John 5:4-5).
That is the faith we need!