Re: Thoughts on this
Is there anything to indicate why she seems to be interested in sex on that particular day and at that particular time?
Example: I am HD and we have sex throughout the week, but we can really take our time on the weekends. That's when I want to dress up and plan something that takes more time and energy. However, DH likes to have a big, naughty, meal on the weekends. Something heavy like a giant plate of nachos. Being full and 3 seconds from a food coma isn't exactly conducive to energetic sex. So, I'd wait to initiate or delay DH's initiation until later in the evening. DH didn't like the delay. He didn't want to feel like he couldn't be spontaneous before 11 pm. He complained that he felt there was too much routine to it. I explained about the food. Now we eat our big, naughty, meal earlier in the evening so we have time to digest and get our 2nd wind before we do anything interesting.
Maybe there is s specific set of circumstances that you could reproduce on other days or some adjustment could be made to allow for a bigger timeframe and buildup.
If you are going to reject her passively, why not do it actively and explain why while you're at it? You said she seems to be upset by rejection. Pain can be a great teacher and motivator. We feel pain and we are motivated to avoid feeling pain in the future. If you explain why you're rejecting her while she is feeling upset, maybe she will begin to understand how much of a problem this really is and be motivated to do something more to avoid being upset in the same way again.
Follow the evidence where it leads and question everything.