I just took a quick look at the theme, since for a change I could actually look at a themes code. The answer is, no, the theme does not use standard WP functions to include template files. What this means is that the standard global variables (like $post) are not available.
I think you can correct this by simply declaring the global variables that you need to access, in this case $post
<?php if(have_rows('otros_archivos')):
global $post; // add this
while (have_rows('otros_archivos')) : the_row();
$post_object = get_sub_field('antecedente');
echo "<ol>";
if($post_object):
$post = $post_object; setup_postdata($post); ?>
<li><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
<?php wp_reset_postdata();
else:
echo "<li>No se ha incluido ningún antecedente aún.</li><br/>";
endif;
echo "</ol>";
endwhile;
endif; ?>
