Luke 11:5-9 (KJV)
⁵ 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;
⁶ For a friend of mine in his journey is come to me, and I have nothing to set before him?
⁷ 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.
⁸ 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.
⁹ 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.

Importunity - shamelessness, boldness, shameless audacity, persistence

While many use the word persistence, this is not the primary / normal use of the word in the original language according to some dictionaries.

Shameless audacity seems to best convey the idea Jesus is expressing. 

Certainly Jesus is not teaching us to be rude when we pray, but rather to be bold.

I would say that most of the time when we think of being shameless it's from the "you should be ashamed of yourself" side of the issue. There is however a positive way of looking t this word and that is being without or free from shame. 

Romans 8:1 (KJV)
¹ There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit. 

If there is no condemnation, there is no basis for shame. So we can approach the throne with boldness, confidence and no sense of shame ... shame-less. 

Luke 11:8-9 (NIV)
8 I tell you, even though he will not get up and give you the bread because of friendship, yet because of your shameless audacity he will surely get up and give you as much as you need.

9 “So I say to you: Ask and it will be given to you; seek and you will find; knock and the door will be opened to you.

Notice, Jesus tells the parable, then the "pay off line" and then He says ASK.

In other words, when you ask in boldness, with confidence, you will get your answer so ASK. 

Ask, seek and knock with boldness, with confidence you will receive, find and have an open door. Those words are "RED LETTERS" and "RED LETTERS" trump everything.

As to the issue of persistence, let me put it this way. In Heb 4:16 we are told come ... to obtain grace and mercy in a time of need. When don't we need grace and mercy? The way to throne is open and we should be using it as often as necessary, as often as possible. Be persistent, be consistent in prayer, Jesus said "men ought always to pray", Paul mentioned prayer without ceasing. So as we pray, when we pray let it be with boldness and confidence, with no sense of shame but standing in the right relationship Jesus has made available to us.

SELAH