Hi! I'll be glad to be of help with this issue.
I can imagine how frustrating and distressing this situation must be for you. You are clearly a good man in a good relationship--except that it's not good at its core. I'm so sorry you are going through this. It's really difficult and frustrating when your lover says she's forgiven you, but she really hasn't. At this point you have no reason to not believe her when she says that the only reason she doesn't want to have sex is because of what you said.
And this is actually the key to my answer to you that you need to consider and think about. There is a possibility here that she really still has a lingering belief that you don't really care about her. And thus, withholding sex is a way to see if you really do care about her or just want her for the sex. I know that's a bit weird because it's been six months already. But sometimes people can get themselves all twisted up in their thinking like that.
The problem here is that your question is a fair one: how long should you keep waiting. The answer really is that you shouldn't keep waiting. We don't know if the thought pattern I described above is what is going on or if there's some other thought pattern making her behave in this way.
But you've tried from what you describe enough really good ways to establish good faith that it now needs some professional intervention. The two of you need to go to couples counseling and find out what is really going on in her mind and heart. Because that she says she's forgiven you, yet holds this grudge is indicating something is not reconciled for her and she can't make it happen on her own or just between the two of you. So you need to get a professional involved.
I don't know if you're willing to. It sounds as though you love her and care for her. So, I would then recommend taking the step of going to couples therapy. But certainly just waiting longer does not seem as though it will change the dynamics that are going on now.
Okay, I wish you the very best!
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I am going to assume, as Dr. Mark has done, that it IS the mean things you said when you were drunk that still come back to her when you're trying to get her to have sex with you. That leads me to 2 separate conclusions.
1. What, if anything, have you done to make sure that you'll never get that kind of drunk with either her or anybody else again? She might be a little more optimistic about your relationship if she saw that you are actually continuing to make sure that your drinking habits have changed--since that's the source of the wound you have inflicted on her feelings towards you.
2. Do you know the feeling state of REMORSE? (This is what an Emotionally Focused Couples Therapist would focus your couples counseling on. For when a partner can't seem to forgive a wound, that's the most likely background--unless something similar has also happened to her from some other guy, or from mother, father, sister or brother.)
There are 2 parts of REMORSE. 1. First you need to get into her shoes and her heart and go through the entire experience inside of her, so you can truly Empathize, by feeling some of what she felt. You might need help to do that. You might be more respectful in her eyes if you just go to an emotionally focused therapist By Yourself first and tell her what you said and ask her to help you feel what that must have felt like. It's pretty unusual for a man to be able to feel as low about himself as a woman can, without just rebounding into anger and aggression against the other person that he's received these insults from.
A woman would have an easier time feeling what your girlfriend felt, because there is more likely to be a deep pit of worthlessness inside of a woman that most men would never dare to visit, unless they've been practicing alcoholics and then spent a few years in Alcoholics Anonymous. IN FACT, EXPERIENCING THIS JOURNEY THROUGH EMPATHY COULD BE EXTREMELY BENEFICIAL FOR YOU, for issue #1 as well as #2.
2. Besides a thorough experience of her suffering so you can empathize, the second thing you need to do is to confess to her and show her what you have felt as you tried to empathize with her. I had to kneel when I have done that. You can also ask her if there's more that she's felt that you don't understand yet (like that she now even feels bad about herself that she can't seem to forgive you, because she knows she's supposed to, and you're being perhaps even better to her than she thinks she has a right to expect from you).
But the ultimate realization that this process will give you is THERE'S NO WAY YOU CAN EVER TAKE THAT WOUNDING EXPERIENCE AWAY FROM HER. You can't undo it. You may have to face that humbling--or humiliating realization with her, or just leave her so that you can eventually forget that it ever happened.
I don't expect you to be happy with what I've written, and I know that true REMORSE that includes admitting that you're powerless to ever take away the memory of what you said is an awfully hard pill to swallow, like a stain that can never be washed off. It's not cowardly to give up on this relationship and just wait and hope to start over again with somebody else. It's enough to just use this ineraseable failure to motivate enough reform in your drinking habits so that nothing like this ever happens again. At least that would be a benefit to you. [You could also use your solo therapy session(s) to find out how you came to express such meanspirited words to the woman you loved, because that could lead downstairs in your mind towards developing a better personality structure for future love relationships.]
A major difference between my approach and Dr. Mark's is that I think it's YOUR responsibility FIRST to look carefully and honestly into the issues in your own mind and behavior (including drinking) that led to this painful incident, BEFORE you try to get your girlfriend's head examined. If you spend the 1-2 sessions it could take to get sufficient insight into your own mistake and to really experience empathy for her and remorse as well as your powerlessness to erase your effect on her, then you could either present what you have learned and what you feel (your remorse and humility) to her in private, or invite her to listen to you in front of the therapist.
Here's the kicker about this path: Whether she's able to get through her hurt or not, YOU will have done something for yourself that very few men have ever done. YOU could end up with a better handle on achieving reconciliation in any deep relationship than you can get with any other approach, AND perhaps also a deeply useful lesson about keeping your balance in the presence of alcohol and other mind- and emotion- altering substances and activities.
It takes more courage and humility than guys normally like to muster up.