I get this question quite often. When Christians realize that God honors a person's freewill choices they naturally begin to wonder what possible good their prayer might do for those who have yet to come to Christ.
But when we pray for those who are lost we are asking God to move powerfully to draw that person to Himself, and to use all of life' situations to further open their heart toward His saving grace and mercy. Furthermore, we are praying for God to use others to challenge and encourage them to properly consider such important matters.
We can scarcely begin to understand all the ways God might answer such a prayer, and even though the final choice remains with the person for whom we are praying, our intercessions are sorely needed on their behalf. Don't stop praying!
QUESTION 2: If I am praying for something and God answers, does that mean He would not have answered that way if I hadn't prayed? (Doesn't God do good things for people simply because He is a good God?)
It's very possible you would not have received an answer had you not prayed. James tells us:
You do not have, because you do not ask. James 4:2c (ESV)
But if we don't receive something from God (due to our not asking) that doesn't mean He isn't good. It simply means we didn't take advantage of His gracious invitation to bring our needs before the throne of grace. Prayer is a privilege, and Jesus told us it works.
If you then, who are evil, know how to give good gifts to your children, how much more will your Father who is in heaven give good things to those who ask him! Matthew 7:11 (ESV)
Notice that verse above ends with the words, "...to those who ask Him!" I suppose God could have arranged things in such a way as to be the mysterious benefactor who sends a support check once a month while never being seen or known. But the fact is, He wants to have a relationship with His children. And although He certainly can work sovereignly on our behalf, responding to our needs even when we haven't sought His assistance, for the most part God desires that we come before Him in prayer. He wants us to talk to Him, and He wants to speak to us in return.
QUESTION 3: If you pray for something for a long time and do not see an answer, how do you know if God wants you to persevere in prayer, or if He is simply saying no?
This is a good question, because I don't believe that the lack of a response from God is the same thing as a "no." What kind of father answers his children by simply ignoring their questions?
Too many times believers give up on prayer, assuming they've received a no, when in fact God wants them to continue seeking His will. Jesus taught about not giving up in prayer. I would encourage you to read Luke 18: 1-8.
The real question ought to be: How long is too long to pray about something? Some prayers have their own expiration date simply because the thing we're praying for is no longer required or the deadline for God's direction is past. But there is a passage in Luke that has always intrigued me concerning prayer, and it has to do with Zechariah, the father of John the Baptist.
We're told that Gabriel appeared to Zechariah while he was on duty in the Temple, and announced the coming birth of his son. The actual words from Gabriel are fascinating because he said: "Do not be afraid, Zechariah; your prayer has been heard. Your wife Elizabeth will bear you a son, and you are to give him the name John." (Luke 1:13 NIV)
Did you catch that? Gabriel said that Zechariah's prayer had been heard. I can imagine Zechariah asking, "Prayer? WHAT prayer?!" It's pretty obvious he hadn't prayed that way for a long time. The text clearly tells us that his wife was past her child-bearing years, and it's also pretty apparent from the passage that Zechariah had no expectation of Elizabeth becoming pregnant, because Gabriel's words were met with nothing but doubt. (Luke 1:19-20)
So Zechariah's prayer had come before God, but wasn't answered until long after he had stopped praying. With that in mind, how long is too long to pray about something? Depending on what you're praying for, I would say keep going until the Lord shows you otherwise.