Here are my assumptions based on what you've posted so far.
You're obviously not a native English speaker (that's ok, neither am I).
You seem to know for certain how English speakers should perceive your words. That's problematic, considering you're not a native English speaker, and yet you don't seem to listen to what some of the better English speakers are telling you in the comments.
Not only the acronym "CP" was inappropriate, but the word itself "counterparty" is inappropriate for the context given. The language you use is way too formal. Even the way you structure your question with assumptions and context is too formal. This isn't your fault. Foreigners are taught formal English and formal structure.
It's the same way Americans are taught formal French, when instead they should be taught conversational French.
or meet in person
Should be "or met in person" with only one 'e'
You're not using "Holding Replies" correctly. You can argue you know how to use that expression, but the grammatical structure you're using is not correct at all.
Your message is very vague. For instance, the following sentence is so vague, it really doesn't mean anything.
In most of our communication, I often do not hear from you for days,
but I understand the necessity of more time before replying.
Most of? For days? More time?
If you want to say something, please say it, but please be more specific. By days, do you mean that she didn't reply to you over the weekend?
mentally distresses and exhausts me,
These words do not work in that context. The term you need to use is "frustrated" as in "I was frustrated by your..."
In most of our communication, I often do not hear from you for days, but I understand the necessity of more time before replying. Despite requesting (in one of my first emails to you) Holding Replies from you to allow me certainty that you received my original emails, I still do not not receive Holding Replies from you. My chasing you for almost every email that I send you, mentally distresses and exhausts me, and suggests your not wishing to communicate with me: is this true? How can we solve this problem?
That block of text is too verbose. it should be broken up into shorter paragraphs/sentences and it should be made much shorter overall.
Here I would suggest that you schedule a twice a week Skype meeting at a set time and at set dates, whether there is something to report or nothing to report (until the project is completed).
Despite requesting (in one of my first emails to you) Holding Replies from you to allow me certainty that you received my original emails, I still do not not receive Holding Replies from you.
It sounds like you're using email as a project management tool. It is not meant to be used that way. Please use one of these tools instead.
Personally, I like Asana, but ideally, you should try using what people in your industry are using (unless they're also only using email).
Also, you may like to use a go-between like oDesk (now called Upwork) assuming she's a contractor. Now, I could ask you if she's a contractor, but you're so secretive, I have a feeling you won't tell me.
oDesk used to take timed screenshots of a contractor's screen and generated a daily working diary out of it, that the contractor could annotate. And I am assuming that Upwork kept that feature.