Duplicate WP-Posts-to-Posts (https://github.com/scribu/wp-posts-to-posts/) connections when duplicating a post using Duplicate Post (http://wordpress.org/plugins/duplicate-post/) or the WooCommerce product duplicator.

duplicate-p2p.php

<?php

add_action( 'dp_duplicate_page', 'dp_duplicate_p2p', 10, 2 );
add_action( 'dp_duplicate_post', 'dp_duplicate_p2p', 10, 2 );

// For Duplicate Product support in WooCommerce:
//add_action( 'woocommerce_duplicate_product', 'dp_duplicate_p2p', 10, 2 );

function dp_duplicate_p2p( $new_post_id, $old_post ) {
    global $wpdb;

    foreach( array( 'from', 'to' ) as $direction ) {
        $opposite = 'from' === $direction ? 'to' : 'from';

        $query = $wpdb->prepare( "SELECT * FROM $wpdb->p2p WHERE p2p_$direction = %d", $old_post->ID );
        $data  = $wpdb->get_results( $query );

        foreach( $data as $p2p ) {
            $meta = p2p_get_meta( $p2p->p2p_id );
            array_walk( $meta, function( &$val ) {
                $val = reset( $val );
            } );

            p2p_create_connection( $p2p->p2p_type, array(
                $direction => $new_post_id,
                $opposite  => $p2p->{'p2p_' . $opposite},
                'meta'     => $meta
            ) );
        }
    }
}