Mark, I know that the sexual intimacy stuff has been an ongoing issue for a while, and I've been in the exact same situation (I'd say my wife and I have averaged maybe 4x/YEAR in our nearly 10 year marriage) so I definitely feel your pain, but you have to realize that you can't, you just can't say that the weeks after giving birth are like any other weeks in your marriage.
The past really doesn't matter in that first few weeks. Remember every pregnancy is totally different too, so you can't compare it to the last. In fact, KNOWING that sex is pretty much off the table for these next few weeks, in that she has a really damn good excuse for not feeling sexy, you should take this OPPORTUNITY to just love her and make her feel beautiful. Show that you have no expectations, don't dare to try to escalate a friendly hug or kiss to anything more. Let her feel comfortable that she can show you affection without fear that you'll try to push her into something she is not comfortable with. It just makes her not want to show any affection that might "set you off".
After that, honestly if you haven't tried it yet, I think you need to give her a vacation from sex. "Dude, the last two years have basically been a vacation from sex for her!" Yeah I know, but I really mean a vacation from sexual expectations. Just straight up tell her that you realize that she probably feels like she is failing you in many ways because of the sexual issue. She probably feels guilty, and even if/when she does feel affectionate towards you, she is probably fearful of expressing it because of how you'll respond to it, which will force her to reject you again and experience that guilt and shame all over again. It's a cycle, and it does nothing but push you both further and further apart. Trying to haul her back into more counselor's and pastor's offices to talk about sex, and how you're unfulfilled, and how it's basically her fault (even if done in the nicest way) is just humiliating and and causes her to feel even worse about herself. All the while wondering if it is just a matter of time before you dump her for someone else who is more attractive or at least willing to be more sexual than she is, despondent in the feeling that she can't keep her husband happy the way most women can, nor could she blame him for possibly wanting someone else if it came to that. Eventually she feels resentful, with very low self confidence, and unloved.
"But dude, I do love her, and I show her that a bazillion different ways!"
I'm sure you do, but woven through every interaction and every nice thing you do, there is the reminder that she is still failing you, or maybe a fear that you do nice things just to butter her up for sex, or she might feel guilty when you treat her well and she can't reciprocate in the way you want most, and so on. Eventually they just become words to her, and before long she just wants out.
So the idea is a sexual vacation. It's gotta be at least three months, probably closer to six. Just be honest about everything above, that you can empathize with her, that you feel like you understand a bit better (though be open to letting her share more if she wants to) and the idea is that maybe you can both rebuild your relationship better if you completely remove the element of sexual intimacy for a while. She can experience your efforts to show her love and affection without fear of an underlying motive. She can feel free to show her appreciation and affection without fear of you trying to escalate it. I imagine she would LOVE such a gesture from you, showing her that you love her enough to willingly sacrifice this element for her for a while, because it is important to you that SHE FEEL the love that you have for her, that she know it is real, and that it ISN'T just because you are horny or otherwise "want some" from her.
Again this is a massive suggestion, and I could be way off base here so feel free to ignore me. But like I said, I bet something like this could mean the world to her. It might take a few weeks before she believes it, but I bet she carries enormous loads of guilt, shame, resentment, fear, etc. on her shoulders every day, so to help her remove all that baggage for a few months, you might be able to jump-start her love and self esteem in a huge way.
One last thing, has porn been an issue for you? As in, do you use porn? If so, does she know about it? Either way, if you use it, you gotta cut that out. That too messes with her in an enormous way. Give that up at the same time and wow, she won't know who you are anymore.