John,
You need copy the data when the OnPostback event fired, and maintain the table by your self.
If you don't use AJAX, the page will be submit and then all javascript data will be lost.
So you should use AJAX.
There's two primary AJAX :
1 - Microsoft AJAX , so you need maintain the data and show the talbe outside the UpdatePanel
2 - Use MvcUploader , and provider another UploadHandler.ashx
(See the MVC-CSharp sample page , Microsoft-MVC is not the must thing, MvcUploader support all asp.net pages)
Here is an advanced samle which tell you how to send data between server and client :
Regards
Terry