She's definitely on the defensive isn't she? Once again, it's to be expected. I suspect she's gotten it entrenched in her brain that any touch from you must mean you want something "sexual"...or at least something more of her. Which in reality you do want something more, you want to have physical contact of some sort....even if it's merely holding her hand, but you might try reassuring her....when she throws up those smoke-screen excuses that all you wanted to do when you reached out for her hand....was to hold her hand, nothing more right then (if that's the case.)
She needs to understand that not all physical contact leads to sex for you. Sure, you may want it to lead to sex at times....but as I know all too well, sometimes just snuggling, holding hands, or a kiss is really all we can be after, just some affection.
I'm sure others on here will have some great suggestions for you as to how to proceed on this too....but for me, right now I'd work on letting her know she's loved (you do this well) and letting her see that just because you want to touch her doesn't mean you ALWAYS want it to go anywhere. So perhaps next time you reach out for her for a hug, a kiss, or even just to hold her hand and she throws up an "I'm tired" at you....tell her, "honey, I just want to hold your hand....or hug you....or give you a kiss, that's all. (or whatever fits at the time).
I know with my H he went through a time where he wouldn't have any contact with me at all...he'd steer clear of me physically....because he really thought all I thought about was sex (because I finally communicated what I needed/wanted)...so anytime I'd try to touch him I'd get the cold shoulder.
I think most of our SO's have gone through this when we've tried to communicate with them about the lack of physical affection or sex in our R's. For a time, until they understand how important it is, it's as if they hear us saying "you're flawed!", "you're wrong!", "there's something wrong with you!"....naturally they don't think they are any of these things so they resist, who wouldn't?
I'm pretty sure you are being very careful not to convey these messages to her, but she's likely to feel this way anyway...regardless of what you say/do. So just be patient, be consistent in your words & actions, and stay loving towards her.
But do prepare yourself for your next conversation, keep mental notes as to what you want to address...you might even want to start yourself a journal, that helps me. I'm able to vent when I need to, write down the positives, and then every now and then go back and read what I've written. There are times I think we're getting nowhere, but then I read through my journal and see the progress we truly have made....and sometimes I see where there's a recurring issue, obviously that issue needs to be addressed; either I need to talk to my H about it, or it's something within me that I need to address.
That's just a tool that I have some success with, it might help you too to get through this.
