For the men out there - if a woman says that she's flattered to be asked but declines the dance and doesn't give a "reason", do you still write her off?
No. Often, I don't even expect to get a reason, or I am far enough to hear her words, or I look at her for a very short time to listen to a reason if the reason is delayed even slightly. I don't insist on a reason. I don't want to push her to lie to me - there may be a real reason that she does not want to say, like a medical one or dislike of me.
I will try again later. I will stop asking after the second or third attempts. I may make one more attempt months later. In the meantime, she may come to me and tell the reason. Often it is surgery, joint problems, not knowing the dance, expected dizziness, wrong shoes, undue influence of a man on her, extreme tiredness. As of now, women haven't approached to say that they dislike me, which is something I am perhaps supposed to deduce?
If you decide that you won't ask her again, but then a later time she asks you for a dance, how do you typically respond?
As if she hasn't refused, but I will not be too friendly, will not chat, joke, or make her feel too good or have fun. I will invite her rarely, and she will be at the end of the desired ladies' list for a given dance. If she can handle this and will continue to ask me, then the relationship might improve without the first writing-off having an effect.
There is also a small percentage of women, who tend to refuse sometimes (without explanation) and accept sometimes. I call them "unpredictable ones" and gradually stop inviting them. I think they are exercising power that way. They disappear from the dance scene quickly.
But the worst are the beginners. They don't know how to behave, while having heard (or read) this and that. Add to this weak knowledge, improper shoes, perhaps shyness, and you will get a total confusion. Please, those who bring a newbie with them - give them an introduction, even if they are well past childhood age.