Was it because of the persistence of the Canaanite woman, that Jesus answered her prayer in Matthew 15:23-28? Maybe.
Jesus said that her faith is great. But why did he said so?
In verse 23, Jesus did not even answer her. But latter we see, that he said her faith is great.
What made Jesus to say that? Is it possible that he saw her persistence and not giving up of what she wanted to receive from God? Jesus very plainly refused to grant her request but latter he did.
We know that Jesus said in other parts of the Bible, that we should be persistent in prayer.
It is possible, that our persistence, shows to God, that we believe that he will answer us. The measure of our persistence, and the length of our persistence, reveals how strong or how big our faith is.
If we have a little faith in the promises of God, then our persistence in prayer, will be not so strong, and not for long.
Our persistence in prayer shows to God, that we believe his promises, and that we believe what he said, therefore, we persist and wait for the answer.
It is possible that sometimes, God does not answer our prayers, just because he wants to see, how much we believe that he will answer us.
If we give up quickly, in our prayer and hope for the answer, that shows to God, that we are not really believing his promises for answering our prayers very much.
The quick giving up of waiting for the answer of our prayer, shows that our faith is little.
It is similar with the case of the blind Bartimaeus.
Bartimaeus was very persistent, to get from Jesus, the answer of his request.
People were trying to stop him going to Jesus, but he continue to shout and ask Jesus to help him. Eventually Jesus paid attention to Bartimaeus, and healed him, by answering his request.
In the Psalms, we can also see that we are told to wait on God. The longer the wait, the longer the persistence, and the stronger our faith appears to be.
Maybe God sometimes makes us to wait, in order to grow our faith, and make is even stronger.