Hi,
Well, there is not option to do that, but it should be doable via using a custom code. Try adding this custom code to the functions.php in your theme/child theme directory. Before editing, please make sure to have a full site back-up just in case!
add_filter('asp_print_search_query', 'aspl_placeholder_modify', 10, 3);
function aspl_placeholder_modify($placeholder, $id, $real_id) {
// Reset to empty, when on the results page, and the results are from a different search instance
if (
( isset($_GET['p_asid']) && $_GET['p_asid'] != $id ) ||
( isset($_POST['p_asid']) && $_POST['p_asid'] != $id )
) {
return '';
}
return $placeholder;
}