adding a page outside wordpress, style sheet address changes

I have a wordpress blog sat in /blog and want to create an index page in the root directory which looks like my wordpress pages. I discovered I could open a page in Safari, save as a HTML file and upload by FTP to my root directory as a test page. The page worked. After a few days the page stopped working and I have been told it’s because the wordpress style sheet address expires.

Is there a way to make this work or am I trying to do the impossible?