Luke 18:1 "And He (Jesus) spoke a parable to them to this end..that men ought always to pray, and not to faint"

The failure to perservere is a common problem in prayer and intercession. We begin to pray for something, raising our petitions for a day, a week, or even a month..but then if we have not received a definite answer, we give up and stop praying for it altogether.
This is a mistake and it can be a trap that leads us to beginning many things but never seeing them completed. Those of us (and I am at the top of the list) who begin praying about something without praying through to a successful conclusion can actually form a habit of failure because we tend to give up in defeat. Defeat then leads to discouragement and doubt, and makes it difficult once you are in that state, to even want to begin something.
I think that so often we forget that God works in hearts. He works on the inside..and we can't see what is going on inside someone's heart. One of the times that I actually did persist in prayer was for a family member. I prayed for this person for years that his life would be changed..that he would come to know Christ. I didn't see any results of it for years. His life did change but for the worst. Something in me just knew I should persist..and after about 20 years, He received Christ into his heart, and God began to change him. Often when I would pray for this person, it would be such a simple prayer.. it seemed like I had said it so many times..it seemed repetitive to me..but God heard those prayers that seemed so meaningless to me..and He was faithful to work in this person's heart..a work went on for years..and I just couldn't see it at the time..but God was faithful.
People often ask how long they should pray. They wonder if they should come to the place where they stop praying and leave the matter in God's hands. I have certainly done that myself many times..but probably more because I felt defeated than anything else. I really believe that we should pray until what we pray for has either been accomplished..or until we have complete assurance in our heart that it will be. In the first instance, we stop because we actually see the answer. In the second, we stop because we believe, and faith in our hearts is as trustworthy as the sight of our eyes.
As we live a life of prayer, we will more and more come to experience and recognize this God given assurance. We will know when to quietly rest in it, or when to continue praying until we receive His answer.