WordPress post next/prev not working

I made some updates in your code. Please, try this updated version.

 <div id="demo">
    <?php 
     $wp_query = new WP_Query( array(
     'category_name' => 'Case Study',
      'posts_per_page' => 1,
     )); 
      ?>
    <?php if ( $wp_query->have_posts() ) : ?>
    <?php while ( $wp_query->have_posts() ) : the_post(); ?>

    <?php the_title(); ?>
    <?php the_content(); ?>

    <?php endwhile; ?>

    <div class="nav-previous alignleft"><?php next_post_link('&laquo; %link', '%title', TRUE); ?></div>
    <div class="nav-next alignright"><?php previous_post_link('&laquo; %link', '%title', TRUE); ?></div>
     <?php wp_reset_postdata(); ?>
    <?php else : ?>
    <p><?php __('No News'); ?></p>
    <?php endif; ?>
    </div>