in absolute simplest case you could save the index of the row to a cookie and on page load either use server or javascript to set the class based on cookie index.
In likelihood this won't be very useful if any changes occur to table before next load such as a row added or deleted above your indexed row
If rows have some identifier you could improve on the system.... it really all depends on how dynamic your table is and what level of accuracy you need
using jquery cookie plugin and indexing:
$("tr").click(function () {
var idx=$(this).index();
$.cookie('rowIdx', idx);
$(this).addClass("selected"); });
then on page load:
var idx=parseInt( $.cookie('rowIdx'));
$("tr").eq( idx).addClass('selected')
EDIT: not sure if this answers the issue or not... perhaps you were trying to figure out how to manage "completed" if so you would need to use ajax()