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Remember, this is the God Who chose to make an eternal covenant with David, who was a murderer as well as an adulterer. God knew all this (since He knows everything and is out of time), yet He chose David anyway and called him "a man after God's own heart." God used Rahab the harlot and the murderers Moses and Paul. He made a cowardly weakling who betrayed Jesus three times the leader of His Church. Jesus immediately forgave the woman caught in adultery, when the Pharisees wanted to stone her (and under the Law, they could rightly have done so). God doesn't give up on people, but they sometimes give up on Him.
Addiction is a particularly difficult and complex problem. The addicted person isn't even totally free in what he does, so in a sense the semi-involuntary nature of the thing one is addicted to is not as blameworthy as, say, a premeditated plot to do some evil.
The sexual or pornography addict must come to a place, like an alcoholic or heroin addict, where they decide they have had enough of the destructive price of sin, and want to change their life. The addict can decide this. People will help. God will pour out His blessing and grace, upon a decision to do this. It's a wonderful place of opportunity: a great place to be: to decide to take back your life and to stop giving in to temptation and lust. Sadly, many people never get to this crossroads of repentance and positive decision. The first step to recovery (from anything) is recognizing that one has a problem to resolve.
If you are reading this now and suffer from addiction, chances are God is already at work in you to help you realize that there is a problem; that you are in a mess and going downhill fast. There is a way out of it. He gave you the conscience to recognize that all is not right, and that this is not the way to a happy and fulfilled life. You can decide right now to start doing something about that, and to make a change for the better. God will give you grace; people who have gone through similar experiences are waiting right now to assist and help you. Check out the following resources:
[Internet discussion board]
Dads.org / St. Joseph Covenant Keepers Recommended Resources
Family Life Center International Resources
Treatment and Healing of Sexual and Pornographic Addictions, Dr. Victor B. Cline
12-Step Recovery Groups
Sex and Love Addicts Anonymous
Sexual Recovery Anonymous
See also this article about 12-step programs with regard to sexual addiction.
Society for the Advancement of Sexual Health (SASH) overview
General Christian Resources
Mastering Life Ministries
Pure Intimacy (from Focus on the Family)
RSA Ministries ("Christ-Centered 12-Step Recovery")
Books on Sexual Addiction (mostly Christian)
Christians in Recovery
Sexual Addiction FAQ