Does the teaching that, instead of praying repeatedly about things, we should claim them in faith only once hold any water?
These teachers often base this claim off of the first half of John 14:13, which says, "And I will do whatever you ask in my name," but leave off the ending: "so that the Father may be glorified in the Son." The context of the chapter is giving the disciples a plan and basis for their ministry after Jesus' death and resurrection. James 4:3 clarifies this for us today: "You ask and do not receive, because you ask wrongly, to spend it on your passions."
So can we in faith pursue God's will through repeated prayer? Jesus teaches us through parable in Luke 18:1-7 that God will move for the sake of justice through persistent prayer. It's in His heart to do so. Luke 11:5-12 is another encouragement toward persistence. We need to understand that prayer, as part of our relationship with God, is conversational and interactive. We can bring our requests to God, but we should expect to hear back and to be changed from the encounter. When we ask for something outside of His will, we should allow Him to realign our will. If the Holy Spirit has moved you to pray, don't give up until you've seen the prayer realized or until you have an answer that shows you God's heart.