Hi,
Well, there is no option to do that, the plugin will automatically fetch the posted options. It might be however possible via a minor custom code snippet.
Try adding this code to the functions.php file in your theme/child theme directory – make sure to have a full server back-up first for safety. For more details you can check the safe coding guidelines.
add_filter('asp_shortcode_search_options', 'asp_reset_options_on_results_page', 10, 1);
function asp_reset_options_on_results_page($settings) {
unset($_POST['p_asp_data']);
unset($_GET['p_asp_data']);
return $settings();
}