Hello everyone.
I had been experiencing the same problems you have in deleting books from my Kindle for the PC. No matter what I did, it would still show up in the Archived Items.
After researching the posts on Google, I finally decided to do something about it.
I have put together a webpage describing the steps where you can delete books from the Kindle for the PC without having to de-authorize your program and then having to re-authorize it and redownload all of your books again.
The link to the webpage with the instructions is:
http://howtodeletebooksfromkindleforpc.weebly.com/
I hope this helps a lot of people. It certainly worked for me.