A very close friend of mine and sister in Christ is suffering from sexual addiction. I don't think it would be appropriate to go too deep into her problem, but to be short she has had sex with at least three different men in the last month, two of them non-Christians. She is simply unable to resist their advances, she says. She has admitted her addiction herself, but is not, I think, prepared to try to recover. What can I as a friend and brother do to help her out of her addiction?

Dear brother, while I do not deny there may be addictive elements present, this is hardly a mere psychological or in any way uncontrollable condition. This sister is acting immorally.  See Hebrews 13:4, and also 12:16 -- she will face God in judgment. These are extremely serious sins. 

If she is too weak-willed to fight, there may be little you can do for her. Repentance is a personal decision. I would be quite strong with her. If she began to read, pray, and think less of her own pleasures, God would give her all the strength she needed to overcome the temptation. 1 Corinthians 10:11-13 assures us this is the case!