Sorry to hear that. I suspect it's quite a common problem, but that doesn't make it any less devastating.
I have a number of thoughts but I appreciate the rantings of some complete stranger who knows nothing about you or your wife might not be very useful.
My first thought is - Is she depressed? The PHQ-9 is useful; www.patient.co.uk/doctor/patient-health-questionnaire-phq-9
My second thought is - Do you make her feel special? Do you compliment her, listen to her problems, support her, do little things for her, have fun together, laugh together, share interests?
My third thought is - Has she gone off you?
Personally I'm not sure I believe in love. I think relationships last because two people get on well together, care for each other, are sexually compatabile, willing to compromise, and lucky enough to change in the same direction as they get older.
I do wonder how much she cares for you if she is not willing to consider going for counselling. It's a horrible situation to be in because you could argue it either way - "If you loved me enough sex wouldn't be that important" or "if you loved me enough you'd be willing to go for counselling". Relationships are about compromise, but it sounds to me like you're doing more compromising than her.
It sounds like this is something that is really getting you down. We all differ in terms of how important sex is in our lives and I guess some people are lucky enough not only to be compatible initially, but stay the same or to change in the same direction as their lives progress.
If you get on well in every other way it seems like a shame to end an otherwise good relationship purely because of a lack of sex, especially when there are children involved. But reading between the lines of your posts it sounds like it is not just the sexual side of your marriage that is not as good as it could be.
I don't wish to seem insensitive, but is it possible she wants you to leave her? Some people can not face ending a relationship and so will just withdraw in the hope that the other party will have the balls to do it. That way they get to be the good guy/girl and don't have to feel any guilt/blame as it wasn't thier fault in everyone elses eyes.
Have you asked her if she is happy with the marriage? Maybe it's time to sit down in a non-accusing way and just ask her. "Are you happy?" "Are you happy with our marriage?" "Would we both be happier if we were no longer together?". You only have one shot at this life and it's too short to drag out a mistake for years and look back at it with regret.
It sounds like you've discussed the sex thing before, and like you say there is no way you can win in this situation unless she genuinely wants to start having sex with you again. You wouldn't be asking her about whether or not she wants to separate purely because you're not getting any sex anymore, you'd be doing it because you genuinely want both of you to be happy human beings. From what you've said at the minute it doesn't sound like that is the case.