Honestly, I don't get it. What does sex really take? You are asking her to lie on her back for less than 10 minutes and let you have her to show you that she cares for you? it is nothing.
The fact that she won't do this has nothing to do with sex. It is about control and resentment, or some past baggage that she won't let go. Seriously, we are not talking about the real issue.
What is the real issue?
Would you entertain that it may be a couples issue, not just the woman's "lack" of something or another? In other words, if this is the situation, the man might have a lot to do with the problem too.
I'm going to have to tell you that your first paragraph above would offend a lot of women, including Christian loving women. Perhaps it doesn't have all the context it should, but if you were a politician, in many areas of the country your career would be over with that paragraph alone.