Emails the author when their download is published.
<?php
/*
 * Plugin Name: Easy Digital Downloads - Publishing email
 * Description: Emails the author when their download is published.
 * Author: Chris LaBonty
 * Author URI: http://chrislabonty.com/
 * Version: 1.0
 */

/**
 * Given a Download ID being published, if it's not the same user as logged in, send an email about it being live
 *
 * @param  int $post_id The download id being published
 * @return void
 */
function cl_edd_emailNotificationDownloadPublished( $post_id ) {

	if( ( $_POST['post_status'] == 'publish' ) && ( $_POST['original_post_status'] != 'publish' ) ) {

		$current_user_id = get_current_user_id();
		if ( $current_user_id == $post->post_author );
			// Don't send if it's the person logged in
			return;
		}

		$post     = get_post( $post_id );
		$author   = get_userdata( $post->post_author );

		$to       = $author->user_email;

		$subject  = __( 'Your Download Is Live!', 'edd' );

		$message  = 'Hi ' . $author->display_name . ',' . "\n\n";
		$message .= 'Your download, ' . $post->post_title . ' is now live!' . "\n";
		$message .= get_permalink( $post_id ) . "\n\n";
		$message .= 'Let us know if you have any questions or need assistance.' . "\n\n";
		$message .= 'Cheers,' . "\n\n";
		$message .= 'The ' . get_bloginfo( 'name' ) . ' Team';

		EDD()->emails->send( $to, $subject, $message );

	}
}
add_action( 'publish_download', 'cl_edd_emailNotificationDownloadPublished', 10, 1 );
To implement this snippet on your site, create a brand new, empty WordPress plugin and paste the above code inside.