Pray until you can honestly say with that hymn writer: Sweet hour of prayer. - Paul Washer
I like to call this "pressing through".
If you are like me, you have often set your knee to pray and felt almost as if your prayers fluttered above your head but weren't reaching heaven--they kinda hit the ceiling and fell back down. This, of course, is our own sinful unbelief getting in the way, because God has promised to hear us (Psalm 65:2); it is our job to believe what He says.
So, what is going to break through that barrier created by our unbelief?
Let me just say, that God is at all times present everywhere (Psalm 139:7), but the unbelieving eye does not have the power to see Him (2 Corinthians 4:4). Just as a blind man can stand in the same room with an elephant and say there is no elephant there, an unbelieving man will always deny the thing right in front of his face because he does not have spiritual eyes to see it.
There is willful unbelief and there is unbelief that is not willful, like that of the father who came to Jesus on behalf of his child who said: "Lord, I believe; help my unbelief" (Mark 9:24). Like that man, we are all tempted to doubt, but we need to recognize it as the sin that it is and not play games with it. We have to act decisively against it and kill it where we find it (Romans 8:13); even so, God does not condemn those in Christ (Romans 8:1). We are safe from condemnation; instead, He chastens us as sons and daughters (Hebrews 12:6).
Yet, knowing that your unbelief (your doubts) make your prayers cold and dead (just as James says: a man who doubts in prayer must not think he'll receive anything from God - James 1:7-8) ought to stir within you the desire to kill that unbelief so that you can pray to the God of mercy. You should want to "press through" beyond the deadness to that place where prayer is sweet and communion with God is real and unbroken.
When I set to "pressing through" I like to sit alone in my room at night with all the lights out so that there's nothing to distract me, sit or kneel on the floor, and just talk to God out loud. I pray until my prayers are a joy again and I don't want to stop. I pray until I know I'm talking to my Best Friend--I'm communing with the Lover of my soul. I pray until I know I'm speaking with a loving Father who cares for me and the people around me. Then my prayers are sweet and easy and it's not so hard to imagine staying up all night like Jesus talking to the Father. [No; I haven't stayed up all night in prayer yet, but it would be sweet; I hope to be able to do that some day.]
What an honour and a privilege it is to pray.