Before the fall of Adam and Eve, man was given authority over God's creation. When Adam and Eve chose to sin, they forfeited their right to this authority and in a sense handed their authority over to the devil. When Jesus died on the cross for our sins and overcame death through the Resurrection, that authority was given back to us. Not only do we once again have authority over God's creation but we can bring God's Kingdom to the earth and earthly situations (Matthew 28:18).
Often times however, we do not realize or act as though we have authority. We do not act as though we are sons, daughters and heirs of the King.
I still have a ways to go in this area but I believe the key to seeing our prayers answered is to first realize the goodness of God; realizing that he is a good and loving Father who wants the best for his children. We also walk in the knowledge of who we are in Him. We do not need to beg God to act; We do not need to beg him because he never holds back or with holds from his children. He is not going to decide to act only after we have prayed for the 100th time. His love and mercy is overflowing and abundant!
The purpose of intercessory prayer isn't to manipulate God into acting but instead is an opportunity for us to come into his presence and exercise our authority as sons and daughters of the King. We have the opportunity to partner with God.
So, if you look at intercession this way, A lot of it is spiritual warfare. Through intercession, we are reminding the devil who our dad is. Through intercession, we are claiming the Kingdom in the here and now and what is rightfully ours. Through intercession we are acting in faith and pushing back the devil.
In Daniel 10 we see how an angel of the Lord was on his way to assist Daniel as soon as he started praying but was detained for 21 days by the prince of Persia who was a demon over that region.
We also see from Daniel 10 that the angel was released immediately to help Daniel because Daniel "set his mind to gain understanding and to humble himself before God."
The reason we persevere in prayer and why the answer to our prayer is sometimes delayed is because we live in a fallen world and the devil prowls around like a lion seeking someone to devour- 1 Peter 5:8. We are in a battle!
Having an understanding that we are at war should change the way we pray. Every time we come into God's presence and interceed, we stand in the gap, push back the darkness, usher in the light and increase in faith! The Good News is we have already won and all we need to do is operate in that authority!