Myślę, że jest to lepsze i czystsze podejście do tego, co próbujesz osiągnąć.

// get_adjacent_post will return $post object
$prev_post = get_adjacent_post(true,'',true);
//Using get_the_post_thumbnail() to get featured image of previous post
$prev_thumbnail = get_the_post_thumbnail( $prev_post->ID, array( 100, 100));

$next_post = get_adjacent_post(true,'',false);
//Using get_the_post_thumbnail() to get featured image of next post
$next_thumbnail = get_the_post_thumbnail( $next_post->ID, array( 100, 100));

the_post_navigation(
    array(
        'in_same_term' => true,
        'next_text' => '<p class="meta-nav">'. $next_thumbnail .'Next Post &rarr;</p><p class="post-title">%title</p>',
        'prev_text' => '<p class="meta-nav">'. $prev_thumbnail .'&larr; Previous Post</p><p class="post-title">%title</p>',
    )
);

OK, powyższe rozwiązanie będzie wymagało dodatkowego filtra next_post_link i prev_post_link oraz zastąpienia szablonu_post_navigation, co nie jest zbyt dobrym rozwiązaniem. Więc w oparciu o twój kod wypróbuj ten. Przetestowałem 3 posty z tej samej kategorii i ich zapętlenie bez problemów.

$prev_post = get_adjacent_post(true,'',true);
if($prev_post):
    $prev_post_id = $prev_post->ID;
    $prev_thumbnail = get_the_post_thumbnail($prev_post_id, array( 100, 100));
else:
    $abjacent_categories = get_the_category(); 
    $ids = array();
    foreach($abjacent_categories as $category) {
        $ids[] = $category->term_id;
    }
    $last = new WP_Query( array( 
        'post_type' => 'post',
        'posts_per_page' => 1, 
        'orderby'         => 'post_date',
        'order'           => 'DESC',
        'category__in' => $ids, 
/* use category__and if you want post to be in all categories as current post. 
For now its happy with one of current post categories. 
Depending on this will give different results at the end so keep that in mind. */
     ) ); 
    $last->the_post(); 
    $prev_post_id = get_the_ID();
    $prev_thumbnail = get_the_post_thumbnail( $prev_post_id, array( 100, 100));
wp_reset_query();
endif;

$next_post = get_adjacent_post(true,'',false);
if($next_post):
    $next_post_id = $next_post->ID;
    $next_thumbnail = get_the_post_thumbnail($next_post_id, array( 100, 100));
else:
    $abjacent_categories = get_the_category(); 
    $ids = array();
    foreach($abjacent_categories as $category) {
        $ids[] = $category->term_id;
    }
    $first = new WP_Query( array( 
        'post_type' => 'post',
        'posts_per_page' => 1, 
        'orderby'         => 'post_date',
        'order'           => 'ASC',
        'category__in' => $ids,     
/* use category__and if you want post to be in all categories as current post. 
For now its happy with one of current post categories. 
Depending on this will give different results at the end so keep that in mind. */
     ) ); 
    $first->the_post(); 
    $next_post_id = get_the_ID();
    $next_thumbnail = get_the_post_thumbnail( $next_post_id, array( 100, 100));
wp_reset_query();
endif;

W przypadku HTML możesz przetestować za pomocą następującego szablonu

<div class="nav-links">
    <div class="nav-previous">
        <a href="<?php echo get_the_permalink($prev_post_id); ?>" rel="prev">
            <p class="meta-nav"><?php echo $prev_thumbnail ?> &larr; Previous Post</p><p class="post-title"><?php echo get_the_title($prev_post_id); ?></p>
        </a>
    </div>
    <div class="nav-next">
        <a href="<?php echo get_the_permalink($next_post_id); ?>" rel="next">
            <p class="meta-nav"><?php echo $next_thumbnail ?> Next Post &rarr;</p><p class="post-title"><?php echo get_the_title($next_post_id); ?></p>
        </a>
    </div>
</div>