With Call History expanded, the "Download" link is in the upper right of the grid.
Click "Download" and then click "Download Call History". You'll then temporarily be able to scroll, sort and display items in the selected days period until you change days selection, collapse Call History or close the webpage.
Could you upload a screenshot of what you do see? You have to join the forum to upload a image. See here for details. Or if it is easier, upload the image to imgur and post the link. If you use Imgur you can edit out the private stuff or use snippet to only select a image that doesn't contain private info.
At the time of my post above, what I said was correct. Since then, a Cox update made it unnecessary. I commented on that update a couple of times including this post I received a notice that the above post was flagged. Since you recently down voted it, you were probably also the one that flagged it. You flagged an old post that was no longer applicable because of a more recent update.