First of all, no, you're not wrong to ask God for His forgiveness. 

Those who wish to follow Christ want very much to please Him and the Heavenly Father.  We read, "This is love for God: to obey his commands…" (I John 5:3) and "Just as he who called you is holy, so be holy in all you do."  (I Peter 1:16) Trying to be holy but being unable to overcome sin can be very discouraging.   And then there is I John 3:6:  "No one who lives in him keeps on sinning.  No one who continues to sin has either seen him or known him."  This scripture might make us question our relationship with the Lord.

But look at some scriptures that the Apostle John wrote earlier in this epistle.  "If we claim to be without sin, we deceive ourselves and the truth is not in us.  If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness.  If we claim we have not sinned, we make him out to be a liar and his word has no place in our lives." (I John 1:8-10)   Also, "My dear children, I wrote this to you so that you will not sin.  But if anybody does sin, we have one who speaks in our defense – Jesus Christ, the Righteous One."  (I John 2:1)  The Apostle John confirms that we sin and that we need Jesus to stand by us when we go to the Father in prayer.  Back to I John 3:6, the Amplified Bible says,  "No one who abides in Him – who lives and remains in communion with and in obedience to Him,

[deliberately and knowingly] habitually commits (practices) sin…"  The key words seem to be deliberately and practices

In the Old Testament there was a difference in the way a person was treated when he committed a sin of negligence or frailty compared to a deliberate or unrepentant sin.  (See Smith's Bible Dictionary, under the heading of "Sin Offering.")  The fact that you seem concerned that your repeated sin will not be forgiven is a good indication that you are truly sorry for, and ashamed of, your sin.

The Apostle Paul  writes, "For what I do is not the good I want to do; no, the evil I do not want to do – this I keep on doing.  Now if I do what I do not want to do, it is no longer I who do it, but it is sin living in me that does it."  Romans 7:19,20  Near the end of the chapter, Paul writes, "What a wretched man I am!  Who will rescue me from this body of death?  Thanks be to God – through Jesus Christ our Lord!"  (Rom. 7:24,25)  It is our complete reliance on our Savior that will save us.

This is not to say that because we have Jesus as our Savior we should give no thought to our sins.  In Rom. 6:1 Paul says:  "What shall we say, then?  Shall we go on sinning so that grace may increase?  By no means! "  And in Rom. 8:13 he says, "For if you live according to the sinful nature, you will die; but if by the Spirit you put to death the misdeeds of the body, you will live."  This means by constant striving, but most of all by constant prayer, and trusting in God's forgiveness and help through Jesus, we will gradually overcome some of our sins and weaknesses.  This will come as we give our hearts more and more to him in consecration.  Paul in Philippians 3:8-10 shows us his mindset:  "…I consider everything a loss compared to the surpassing greatness of knowing Christ Jesus my Lord, for whose sake I have lost all things.  I consider them rubbish, that I may gain Christ and be found in him, not having a righteousness of my own that comes from the law, but that which is through faith in Christ …. I want to know Christ and the power of his resurrection and the fellowship of sharing in his sufferings, becoming like him in his death." (Italics added) 

We will never be completely free from sin in this life.  But as our love for God grows, it will replace our love of worldly influences, and we will find joy and strength to overcome, if we keep trusting in Him.