And he spake a parable unto them to this end, that men ought always to pray, and not to faint; Saying, There was in a city a judge, which feared not God, neither regarded man: And there was a widow in that city; and she came unto him, saying, Avenge me of mine adversary. And he would not for a while: but afterward he said within himself, Though I fear not God, nor regard man; Yet because this widow troubleth me, I will avenge her, lest by her continual coming she weary me. And the Lord said, Hear what the unjust judge saith. And shall not God avenge his own elect, which cry day and night unto him, though he bear long with them? I tell you that he will avenge them speedily. Nevertheless when the Son of man cometh, shall he find faith on the earth?
But, an accurate translation of this passage, brings to light a nuanced meaning.
And He also spoke a riddle to them to teach it is always right to pray, and not to be remiss, saying, A certain judge was in a certain city, not revering God and not respecting man. And a widow was in that city, and she came to him, saying, defend me from my adversary. And at first he would not. But a bit later he said to himself, Even if I do not revere God, and do not respect man, yet because this widow hands me sorrow, I will defend her, so that in the end she will wear me down. And the Lord said, Hear what the unrighteous judge says; and will God not at all execute the defense of His chosen (those crying to Him day and night) and will he hesitate with them? I say to you that He will defend them immediately.
The intent of the parable is not to teach persistence in prayer, but prompt regularity. The message is not that God will respond to annoying persistence, but that, if a unrighteous man will respond promptly (if only to avoid an annoyance), all the more so will God respond immediately.
The parable follows a similar (and similarly misunderstood) parable, the parable of the persistent friend (Luke 11:5-10):
And he said unto them, Which of you shall have a friend, and shall go unto him at midnight, and say unto him, Friend, lend me three loaves; For a friend of mine in his journey is come to me, and I have nothing to set before him? And he from within shall answer and say, Trouble me not: the door is now shut, and my children are with me in bed; I cannot rise and give thee. I say unto you, Though he will not rise and give him, because he is his friend, yet because of his importunity he will rise and give him as many as he needeth. And I say unto you, Ask, and it shall be given you; seek, and ye shall find; knock, and it shall be opened unto you. For every one that asketh receiveth; and he that seeketh findeth; and to him that knocketh it shall be opened.
In the Hebrew culture, if a stranger (much less an acquaintance) arrived at your door in the middle of the night, hospitality was mandatory. Anything less would be certain shame to a host. A better translation of this parable is:
And He said to them, Who of you shall have a friend come to him at midnight and say, Friend, lend me three loaves. For a friend of mine has arrived to me from a journey, and I do not have anything that I may set before him. And answering from within you would say, Do not cause me troubles. The door has already been shut, and my children are, like me, in bed. I cannot rise up to give to you. I say to you, Even if he will not get up and give to him because he is a friend, yet because of his shame, he will get up he will give him as much as he needs. And I say to you, Ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you. For each asking receives, and the one seeking finds, and to the one knocking, it will be opened.
The point that Yeshua makes is not persistence, but, again, the opposite. If a human will rise in the middle of the night to help a friend (if for no other reason but to avoid shame), how much more will God, who loves his people, go out of his way to give to the asker?