Hi,
I'm sorry to hear about your troubles in marriage. It's perfectly normal that it would bother you if your wife is defrauding you of a sex life. Does she have any medical issues to deal with?
I'm also wondering what the falling into sin issue you mentioned is. Since you are posting anonymously, I'll ask you here on the forum? What is falling into sin? Picking up girls at a bar? Porn and 'taking care of yourself'? Looking lustfully at women and not acting on it further than that? All these things are bad, of course.
One thing to consider is how attractive you are to her. Have you let yourself go? You can exercise, dress better, lift weights and bulk up, grow one of those two-day beards, shave your beard, or whatever you think might make you more attractive for her. If the intimacy stopped right after the wedding, maybe she didn't marry you for physical attraction, or maybe the problem is a low sex drive combined with selfishness. Do you know if she was raped at some point, or abused as a child, or any of those kinds of things? if she was, she may need some other help. Most of what I write here would apply most to low sex drive and selfishness.
I think this is a situation where you have to be firm. Talking to her with tears in your eyes isn't working, and it probably isn't going to help her be more attracted to you. Women may say they want a sensitive man, but showing too much 'sensitivity' can be a turn-off. You could keep initiating and act like you don't care that she rejects you, and initiate again a little while later.
I know there are some men, who, if placed in this situation, would tell their wives they didn't get married to pay rent for their roommate, they got married to have a wife, and having sex is a big part of that. Then, they'd threaten to divorce if she didn't shape up. If I were in that situation, I wouldn't do that. I don't see it as Biblical grounds for divorce, certainly not to remarry. Though it is a sin if she is defrauding her husband of sex for no reason.
I do think you should be firm with her about it. I know of one man whose wife wouldn't sleep with him, so if she wasn't going to sleep with him, she couldn't sleep in the bed with him. He told her to go sleep in the spare bedroom. He wasn't going to leave the master bedroom either, since she was at fault. I'm not going to say the man was sinning, but that would probably be a bit harsh for me personally. The borderline on this sort of thing is that the husband love his wife as Christ loved the church and gave Himself for her. Another constraint is that husbands are told not to embitter their wives. There are ways to be firm and stand your ground on the issue without doing this, and how you deal with it will depend on what your wife is like. Something that may embitter one woman may not embitter another woman.
I don't think you should stop initiating. I think you need to keep the issue going as an unresolved, ongoing issue in your marriage until she fixes it. You can tell her, "I married you to have a life-long lover, not a roommate." You can tell her, "This is a big problem. This is an area where you are not being a good wife. Don't think that everything is okay between us. It won't be until you start doing what is right in this important area in our marriage." Let her know she's being selfish. If the issue is past abuse, you may not want to take such a hard-lined approach. If the issue is her controlling how often you guys are intimate, make sure she knows its a problem.
I read that a woman brought charges against her husband once in a Puritan church in colonial times in New England for defrauding her sexually. I don't see a problem with that. Unfortunately, many churches totally ignore church discipline issues. But it is something to consider. When you talk seriously with your wife, assuming she is a Christian, you can point out her responsibilities (and you own) in I Corinthians 7. Discuss Matthew 18 with her. If she won't hear I Corinthians 7, then bring two or three witnesses and tell her you plan to bring the issue before the church. If you both are active and your church has a form of congregational government, you might actually be able to do this. The point, of course, is to get her to repent, not to get her kicked out. So if you can do it any other more gentle way, do that.
If you do something like this, it's important to make sure there is no log in your own eye. You need to make sure you aren't falling into sin yourself. Your wife neglecting you may make it easier for you to be tempted, but you are still responsible before God. This could come up if you go the church discipline route, too.
I suppose you could also tell your wife if she keeps this up, you won't hide her sin, including at family gatherings where her parents are present. If she wants people to think she is a perfect wife, you aren't going to go along with it. That's only something you can do if you are willing to bring it up.
Another approach is to get her around some godly women, maybe older women, who take seriously the issue of sexual responsibility in marriage. There may be some books or forums online you could point her to if she will read them. You can also get some Christian books on marriage that address this issue, or one of those Dr. Laura books. It may mean more to her if other Christians, or supposed experts-- who aren't her husband trying to get sex from her-- promote the idea that spouses are supposed to take care of each others' sexual needs.
You can't have serious conversations like this all the time. She probably won't want to have sex right after one, but you can keep up initiating. If flowers, candy, and moonlit walks on the beach, try a more macho approach. See if there is something she responds to.