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So if your partner rarely is in mood for intimacy (once a month if I'm lucky), what is solution?

theres probably no silver bullet... .

how long has this been going on in your relationship, and what, if anything, led up to it?

Intimacy is difficult with BPD.  You're fighting their internal images of themselves, projected onto you, as well as any real issues you may have.  Their feelings = facts, so if they believe they are unattractive and blame you for them feeling unattractive, well, it's obviously all your fault so fix it yourself and don't complain (<-- sarcasm). 

You could be battling perceived slights you don't even know about, like you were busy once five weeks ago when she was in the mood, which has now translated to "he doesn't like me" forever. 

Can you share more about what she says when you try to initiate?  Or if you just wait for her and it never happens?  Are you close emotionally at this time, or pretty often?  Do you enjoy non-sexual affection?  Sitting together on the couch, hugs, holding hands? 

Also, may I ask what the age range is?  I can say as a 41-year-old woman my libido and body have done weird things to me as years have progressed.  Hormones are a BIG factor, and any changes in them, regardless of her age can cause changes to libido, self-image, whether sex is painful, etc.  My left thigh now registers intense almost pain-signals on any touch.  It just started out of nowhere, it's perplexed my BPD H, he assumed it means I don't like him, etc.  No.  I have just developed allodynia as part of my migraine symptoms, where normal touch can hurt, and it's not limited to my head.  I also developed an instant allergy to a massage oil we've used for years.  Sudden burning kinda of ruins the mood 
Your body being against you is annoying and frightening. 

I agree there could multiple reasons why you can't be as intimate as you would like. Starting from rational to totally irrational reasons. My best advice is to probe all likely issues without compromising yourself.

I can tell you from my situation, I wish had that amount of frequency, but I love my wife dearly. The triggers from day to day changes. The lame excuses helped by enablers doesn't help. Break down each reason and have an answer to it. If you can get help from a cooperative third party would help greatly.  I'm all by myself so I'm all alone, but I never give up. Don't give up either especially if the love is worth it

Hmm. Are you saying what I think... .

Hello Steve. I am a Steve too. I'm on the once or twice a month 'plan'.

I get the "we don't have a sex life" comment often, yet she instigates very little. When the drought breaks, it pours, and when it does I say, "We should be doing this everyday". To begin with we did. Then she started to tell me that I'd rather have sex with my ex, who I had split with a eight years earlier. I went several years after that relationship ended, with no sex at all. Pretty sad really.

I don't know what the answer is. It's all my fault anyway! Just enjoy it while it lasts? What's it like when it happens, if you don't mind the question? Is it something you can try and build upon? If we can just have some sexual intimacy a couple more times a month, we would have doubled (or more) our rate. And they think we don't enjoy it, or like them. I am not sure about you; I think about it most days. It just rarely happens. I wonder what we are doing wrong, if anything, or how we can approach this better. Maybe the non-sexual affection is something to consider. That is something I might focus more on.

slowsteve, , I don't mean an affair. Gosh if things were that simple and didn't come with problems. I mean to say someone to be a go-between to relay information and how they think and what you're trying to accomplish. A shared friend, family member and the (wait for it) therapist. BPDs do love the word therapist  a

I am understanding Hart_Payne to be saying a close trusted friend who talks to both of you and might be able to share info that can help you determine what today's current reason is.  Or, communicate on your behalf, gently, using validation and all the tools they can muster.

Any insight into her mind that isn't coming to you already can help greatly.