Get latest author posts inside the loop

I think you are executing reset_postdata() too early, using the global $post object incorrectly inside the secondary loop and passing wrong argumentes to the secondary loop. Try this.

Put the function to get the latest author posts in the functions.php file:

function the_latest_author_posts($post) {

        //some content goes here regarding the post itself!!!
        $relatedargs = array(

             'author' => $post->post_author,
             'post__not_in' => array( $post->ID),
             'posts_per_page' => 3

        );

        $relatedquery = new WP_Query( $relatedargs );

        while($relatedquery->have_posts()){
             $relatedquery->the_post(); 
             $ID = get_the_ID();
        ?>

             <div class="span3">

             <?php
                  if(has_post_thumbnail()) { 
                       $relatedthumbnail = wp_get_attachment_image_src( get_post_thumbnail_id($ID), 'medium', false);
                       $relatedthumbnail_large = wp_get_attachment_image_src( get_post_thumbnail_id($ID), 'full', false);
?>

                       <div class="hover_colour"><a href="https://wordpress.stackexchange.com/questions/117081/<?php echo $relatedthumbnail_large["0']; ?>" rel="prettyPhoto"><img src="<?php echo $relatedthumbnail['0']; ?>" alt="<?php the_title(); ?>" /></a>
                       </div>

                 <?php } ?>

                       <h6><a href="<?php the_permalink(); ?>"><span><?php the_title(); ?></span></a><br><i class="icon-time muted"></i> <?php echo get_the_time('j') . "https://wordpress.stackexchange.com/" . get_the_time('m') . "https://wordpress.stackexchange.com/" . get_the_time('Y') . ' '; ?> <i class="icon-comments muted"></i> <a href="<?php the_permalink(); ?>"> <?php comments_number(0 . __(' comments','textdomain'), 1 . __(' comment','textdomain'), '% ' . __('comments','textdomain')); ?></a></h6>

               </div>

    <?php }
    wp_reset_postdata();
}

Then, in your theme, inside the loop, you can call the function wherever you want to display latest posts from the author of the current post:

<?php
if ( have_posts() ) {
    while ( have_posts() ) {
        the_post();
        //some content goes here regarding the post itself!!!
        //some content goes here regarding the post itself!!!
        the_latest_author_posts($post);
    }
}
?>