add_action( 'init', 'init_no_zero_notifications' );

function init_no_zero_notifications() {
    add_action( 'affiliates_referral', 'no_zero_notifications', 9 );
    add_action( 'affiliates_updated_referral', 'no_zero_notifications', 9 );
}

function no_zero_notifications( $referral_id ) {
    global $wpdb;
    $referrals_table = _affiliates_get_tablename( 'referrals' );
    $amount = $wpdb->get_var( $wpdb->prepare( "SELECT amount FROM $referrals_table WHERE referral_id = %d", $referral_id ) );
    if ( floatval( $amount ) <= 0 ) {
        remove_action( 'affiliates_referral', array( 'Affiliates_Notifications', 'affiliates_referral' ) );
        remove_action( 'affiliates_updated_referral', array( 'Affiliates_Notifications', 'affiliates_updated_referral' ) );
    }
}