He may be your best friend and you may think you know him very well, but if he doesn’t see it as a big problem that the two of you are only having marital relations once every three months, I’d suggest you see a counselor. I don’t know how you’ve been talking about this, but there are some “big ideas” that are not being communicated.
One of those ideas is that the desire for sex is not all about him. People who care about their spouses are willing to “work up a certain enthusiasm” in order to have sex on a reasonably frequent basis. A counselor can help you explain that this is important, why it is important, and that yes, your husband can decide to do something about it.
I would not give you different advice if you were a man. It sounds old-fashioned, but there is a reason that sex in marriage is not just a privilege but a duty. The spouse who is being deprived cannot demand as if the withholding spouse is an object, but this form of affection is one of the duties of marriage.
“The husband should fulfill his duty toward his wife, and likewise the wife toward her husband. A wife does not have authority over her own body, but rather her husband, and similarly a husband does not have authority over his own body, but rather his wife. Do not deprive each other, except perhaps by mutual consent for a time, to be free for prayer, but then return to one another, so that Satan may not tempt you through your lack of self-control.” 1 Cor. 7:3-5
The existence and duration of this problem suggests that the two of you need to grow in your understanding of each other. When a husband and wife understand each other, one doesn’t avoid kissing the other so he can avoid his wife’s reasonable hope that they will have sexual relations. His wife doesn’t read tea leaves to figure out what is up with him; she asks questions to find out why he doesn’t want to exert himself to want to have sex with her.
A mere “I don’t happen to feel like it” doesn’t cut it. That is clueless. He may as well say, “I don’t feel like having a job” or “I don’t feel like telling you I love you” or “I don’t feel like spending any time developing a relationship with our children.” After all, if he didn’t feel like having a relationship with his son, if he didn’t want to exert himself to do things he didn’t like doing because it would be so meaningful to your son, wouldn’t you think something was pretty “off” with him as a dad? Well, you aren’t any different. This is a vital part of your relationship, you need it, and he needs to be reminded of that.
In other words, he doesn’t have to love sex in order to have an active sex life with you. He only needs to love you. If he has a problem that prevents that, you two need to bring that out in the open, head on. It is not fair to leave you needy and in the dark.
I hope that if he has sex with you not because he is overcome with a natural sex drive but because he loves you and wants to please you that you won’t feel that is a form of rejection or that this isn’t “good enough.” That is a great act of love, and it ought to be appreciated as such.