Well, I often hear things like that. My wife is also the one, who wants to do it less often than me. But it's more like 3 weeks are long. Happens, but mostly when someone is ill or the kids etc.

So the first question is:

If you opt out of initiating sexual contact, do you cuddle, kiss or are in some other way nice and cute to each other? Often in sexless marriages this still happens and if your marriage is of this kind, then you still share intimacy and are connected, but sex is fucked up. In these scenarios I highly bet she does not orgasm and you either don't care or do not even recognise fake orgasms. In this scenario you need to learn how to satisfy her. Turn it into a game and make a deal. The game is that she does not have to satisfy you, you have to get her to orgasm. The deal is that she can stop anytime and you won't annoy her for that. But if she orgasms, then fair enough, it is time for your pleasure as well. She might be like "nah I'm out" and then you have to accept that and next time try again.

She needs to unlearn that your sex is crap. And you need to learn how to turn her on. If with this approach you start having a sex life again, then you can play the next good game, that is both try to satisfy each other and can at anytime say stop. Saying stop means the other one is less active and the stop sayer becomes active in pleasuring. Whoever orgasms first, then has to obey the orders of the other in order to get him/her to orgasm. This game will only work after it is somehow working again between each of you, but then it can do wonders, because once you both get better at this game, you will learn to orgasm together and if someone fucks up, learns the desires of the other one...

But you might also be in a marriage where nothing of intimacy happens at all, where basically is no connection and both share some kind of life in the same flat, with the same kids. That is an absolute dramatic situation, in which of course there is no point at all to approach and try to have sex. Men can often do this much better as sex without connection and trust is more natural for men than for women. However in that case you both have to talk and answer the question if you want to establish your relationship again or not. If not, then what's the point? Why accept sexless marriage? Find a new partner. If yes, then get counseling. You are not going to dig out of this by yourself as you have already deepened the gap between you so much that you should have long ago realized you need counseling.