What does "Pray without ceasing" really mean?

From John Piper's "When I don't Desire God:"

And we urge you, brothers, admonish the idle, encourage the fainthearted, help the weak, be patient with them all. See that no one repays anyone evil for evil, but always seek to do good to one another and to everyone. Rejoice always, pray without ceasing, give thanks in all circumstances; for this is the will of God in Christ Jesus for you. (1 Thess. 5:14-18)

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Praying without ceasing means at least three things. First, it means that there is a spirit of dependence that should permeate all we do. This is the very spirit and essence of prayer. So, even when we are not speaking consciously to God, there is a deep, abiding dependence on him that is woven into the heart of faith. In that sense, we "pray" or have the spirit of prayer continuously. 

Second-and I think this is what Paul has in mind most immediately-praying without ceasing means praying repeatedly and often. I base this on the use of the word "without ceasing" (adialeiptøs) in Romans 1:9, where Paul says, "For God is my witness, whom I serve with my spirit in the gospel of his Son, that without ceasing [adialeiptos] I mention you." Now we can be sure that Paul did not mention the Romans every minute of his waking life, or even every minute of his prayers. He prayed about many other things. But he mentioned them over and over, and often. So "without ceasing" doesn't mean that, verbally or mentally, we have to be speaking prayers every minute of the day in the fight for joy. It means we should pray over and over, and often. Our default mental state should be: "O God, help . . ." 

Third, praying without ceasing means not giving up on prayer. Don't ever come to a point in your life where you cease to pray at all. Don't abandon the God of hope and say, "There's no use praying." Jesus is very jealous for us to learn this lesson. One of his parables is introduced by the words, "And he told them a parable to the effect that they ought always to pray and not lose heart" (Luke 18:1). He knew our experience in prayer would tempt us to quit altogether. So he, along with the apostle Paul, says, Never lose heart. Go on praying. Don't cease. 

So from the context of 1 Thessalonians 5 I say that the key to "rejoice always" is to "pray without ceasing." Lean on God all the time for the miracle of joy in your life. Never give up looking to him for help. Come to him repeatedly during the day and often. Make your default mental state a Godward longing for all that you need, especially for spiritual desires.

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Piper's analysis reminds me of R.C. Sproul's writing on understanding what is the will of God. He divides God's will into two concepts: the decretive and the preceptive.

The decretive will of God is:

Theologians describe as the "decretive will of God" that will by which God decrees things to come to pass according to His supreme sovereignty. This is also sometimes called "God's sovereign efficacious will"; by it, God brings to pass whatsoever He wills. When God sovereignly decrees something in this sense, nothing can prevent it from coming to pass.

The preceptive will of God is:

On the other hand, there is a will that can be broken: "the preceptive will of God." It can be disobeyed. Indeed, it is broken and disobeyed every day by each one of us.

The preceptive will of God is found in His law. The precepts, statutes, and commandments that He delivers to His people make up the preceptive will. They express and reveal to us what is right and proper for us to do. The preceptive will is The preceptive will of God is found in His law. The precepts, cepts, statutes, and commandments that He delivers to His people make up the preceptive will. They express and reveal to us what is right and proper for us to do. The preceptive will is God's rule of righteousness for our lives. By this rule we are governed.

Here is the problem with most of us, that which we must fight against daily:

One of the great tragedies of contemporary Christendom dom is the preoccupation of so many Christians with the secret decretive will of God to the exclusion and neglect of the preceptive will. We want to peek behind the veil, to catch a glimpse of our personal future. We seem more concerned with our horoscope than with our obedience, more concerned with what the stars in their courses are doing than with what we are doing.

- Select passages taken from R. C. Sproul. Can I Know God's Will?

The ideas combined translate into the following. We need to be less preoccupied with the decretive will of God, more enthralled and consumed by the preceptive will of God, and one of the most applicable solutions to solving this fight in our divided attentions is in the practice of praying without ceasing, praying often, repeatedly, and to never give up on it. Even when we don't feel its impact emotionally, prayer plunges us into the streams of life, "like a tree planted by streams of water that yields its fruit in its season, and its leaf does not wither. In all that he does, he prospers." (Psalm 1:3)