As a formerly LL person with my ex husband, I will give you my perspective:
When one is LL, they grapple for a reason why. I think the reason I came up with was that I was chronically tired from commuting 1hr each way to work. (a reasonable explanation, yes?) We actually decided to move closer to the city to try and relieve my tiredness. As it turned out, I ended up leaving the marriage before the move could happen.
However, had the move eventuated, we would have discovered that commuting wasn't the problem. And, like you, my ex would likely have been asking what my new excuse would be.
Thing is, we can only take an educated guess at what the problem is. As in any problem in life, we change the thing which is most likely to cause it... and then see if the problem goes away. If the problem doesn't get corrected we need to keep looking for a cause. To put it in practical terms, it's no different to the diagnostics for fixing a PC which isn't working properly.
How is your marriage in general? Could her libido be affected by any issues in the marriage?
We have our ups and downs like most couples.
That's really sad. I can fully understand where you're coming from and why you're so frustrated. Her refusal to seek help would only make things worse - as you say, like she doesn't want to get it fixed.
And the strictly vanilla sex can't be making the idea any more attractive to your wife...she's her own worst enemy! Getting active and trying new stuff is what keeps it interesting.
When I was LL with my ex, I didn't mind physical touch. I loved a cuddle on the sofa or spooning in bed. But I guess that was because he didn't try to initiate sex with me....I had no reason to move away from the affection. Mind you, it was HIM who didn't want to spend quality time together. I craved a 'date night' or just going out and having fun with friends. But he turned sour after we married and continuing our pre-marriage fun was not to be.
Have you considered she may have also hoped her libido would change with the weight loss? She may be as disappointed as you, but hasn't verbalised it.
I would be wary about brining another child into this. If she's already too tired, another child is going to make things worse. My kids are now 12 and 10, but it took YEARS for my libido to get back to average. I'd guess that my kids were 4 and 6 before I felt significanly recovered from the tiredness of being a mother. At mother's group, we joked about our second kids being immaculate conceptions. Even now though, I still get very tired (hence me saying I'd still prefer a good night's sleep if I'm exhausted). Our 12yo is autistic, so we'll never truly escape from the exhaustion of caring for kids.
One of the things hubby does do for me which helps my libido is letting me have a nap on weekend afternoons. He looks after the kids while I catch up on some zzzzzs.
You've been given a rare opportunity to make quick improvements to your love life. Here's why: having taken the initiative to improve herself physically, she will be very open to feedback and validation.
You've always validated her physically by desiring sex with her, whether she felt she deserved it or not, to the point of becoming overwhelming and even annoying to her. So now that she is changing herself for the better, change the script on her. STOP validating her and start redirecting that sexual energy to something else: improving yourself, hobbies, friends, kids, anything but her.
You need to give her libido space to expand right now when it's most primed to do so. Constant sexual neediness won't allow it to expand otherwise. You have been suffocating her libido whether you realize it or not. Like feeding oxygen to a simmering flame, back off for a bit and watch her libido flare back again!
One thing I edited out in my response to you, is that I am sterile.