I tried the stateSave option and it worked great - but ran into problems because it ends up overriding the initial sorting when the page is loaded next time.
My table initialization code looks like this.
$('#ResultsTbl').dataTable( {
"bPaginate": false,
"bSortable": true,
"bDestroy": true,
"bFilter": false,
"stateSave": true,
"bInfo": false,
"aaSorting": [[8,'asc']],
"oLanguage": {"sZeroRecords": "", "sEmptyTable": ""}
});