Hi,

If your popular posts weekly/monthly data can't be updated - that means your hosting doesn't support function: wp_schedule_event from WordPress. It makes the post data can't be removed after each week/month.

Here are our codes to process to clear post views after each week/month:

/**
 * Add schedules intervals
 *
 * @since  2.5.1
 *
 * @param  array $schedules
 *
 * @return array
 */
add_filter( 'cron_schedules', 'penci_add_schedules_intervals' );
if ( ! function_exists( 'penci_add_schedules_intervals' ) ) {
    function penci_add_schedules_intervals( $schedules ) {
        $schedules['weekly'] = array(
            'interval' => 604800,
            'display'  => __( 'Weekly', 'soledad' )
        );
        $schedules['monthly'] = array(
            'interval' => 2635200,
            'display'  => __( 'Monthly', 'soledad' )
        );
        return $schedules;
    }
}
/**
 * Add scheduled event during theme activation
 *
 * @since  2.5.1
 * @return void
 */
add_action( 'after_switch_theme', 'penci_add_schedule_events' );
if ( ! function_exists( 'penci_add_schedule_events' ) ) {
    function penci_add_schedule_events() {
        if ( ! wp_next_scheduled( 'penci_reset_track_data_weekly' ) )
            {wp_schedule_event( time(), 'weekly', 'penci_reset_track_data_weekly' );}
        if ( ! wp_next_scheduled( 'penci_reset_track_data_monthly' ) )
            {wp_schedule_event( time(), 'monthly', 'penci_reset_track_data_monthly' );}
    }
}
/**
 * Remove scheduled events when theme deactived
 *
 * @since  2.5.1
 * @return void
 */
add_action( 'switch_theme', 'penci_remove_schedule_events' );
if ( ! function_exists( 'penci_remove_schedule_events' ) ) {
    function penci_remove_schedule_events() {
        wp_clear_scheduled_hook( 'penci_reset_track_data_weekly' );
        wp_clear_scheduled_hook( 'penci_reset_track_data_monthly' );
    }
}
/**
 * Reset view counter of week
 *
 * @since  2.5.1
 * @return void
 */
add_action( 'penci_reset_track_data_weekly', 'penci_reset_week_view' );
if ( ! function_exists( 'penci_reset_week_view' ) ) {
    function penci_reset_week_view() {
        global $wpdb;
        $meta_key = 'penci_post_week_views_count';
        $wpdb->query( $wpdb->prepare( "UPDATE $wpdb->postmeta SET meta_value = '0' WHERE meta_key = %s", $meta_key ) );
    }
}
/**
 * Reset view counter of month
 *
 * @since  2.5.1
 * @return void
 */
add_action( 'penci_reset_track_data_monthly', 'penci_reset_month_view' );
if ( ! function_exists( 'penci_reset_month_view' ) ) {
    function penci_reset_month_view() {
        global $wpdb;
        $meta_key = 'penci_post_month_views_count';
        $wpdb->query( $wpdb->prepare( "UPDATE $wpdb->postmeta SET meta_value = '0' WHERE meta_key = %s", $meta_key ) );
    }
}

You can contact your hosting provider and requirement them fix it to help you.

We've checked it many times before to make sure this function working well. I saw some customers have this issue before because their hosting doesn't support it.

Best Regards,

PenciDesign