How to draft posts after being published with x days

Question

I would suggest you use wp_schedule_event() and create a custom hook that you trigger daily. This hook can then call a custom function in which you query posts with the desired publish date, and change their status.

For example, create a new plugin and add (note: I have not tested this):

// Schedule auto-drafting post event on plugin activation.
register_activation_hook( __FILE__, 'schedule_auto_draft_posts' );
add_action( 'auto_draft_posts', 'draft_posts' );
function schedule_auto_draft_posts() {
    wp_schedule_event( time(), 'daily', 'auto_draft_posts' );
}

// Draft published posts based on the post's publish date.
function draft_posts() {

    $old_status="publish";
    $new_status="draft";

    // Example: get published posts made before last week.
    $posts = get_posts(
        array(
            'date_query' => array(
                array(
                    'column' => 'post_date_gmt',
                    'before' => '1 week ago',
                ),
            ),
            'fields' => 'all',
            'numberposts' => -1,
            'post_status' => $old_status,
        )
    );

    foreach ($posts as $post) {

        // Update the post status.
        wp_update_post(
            'ID' => $post->ID,
            'status' => $new_status,
        );

        // Fire actions related to the transitioning of the post's status.
        wp_transition_post_status( $new_status, $old_status, $post );
    }
}

// Clean the scheduler on plugin deactivation.
register_deactivation_hook( __FILE__, 'unschedule_auto_draft_posts' );
function unschedule_auto_draft_posts() {
    wp_clear_scheduled_hook( 'auto_draft_posts' );
}

Documentation:

Understanding WP-Cron Scheduling
If you would like to retrieve posts with your own date query, you could use PHP’s relative date formats.

Documentation of the functions used: