You should clone, manipulate, then append.
// clone
var elem = $("#listParticipat.jsParticipantRepeat ").clone();
// your manipulation code here
$(elem).attr('recid', custIDNum);
$(elem).removeClass("jsParticipantRepeat");
$(elem).removeAttr( "id" );
// then append
$(".jsParticipantPlaceHolder").append(elem);