Delete button not working on forum comment
There is a bug report about this

According to one of the comments written by Ravathi.M


  i am also having the same issue the comment wraper class is
  missing.for the initial execution.then i have added the
  ajax-comment-wraper class by custom js code.now it is working fine


Looks like the solution is that you need to add the ajax-comment-wraper comment-wrapper-[post#] class name to your forum comments.  

Go to /sites/all/modules/advanced_forum/styles/naked folder and replace the advanced-forum-naked-post.tpl.php with this code:  

&lt;?php

/**
 * @file
 * Theme implementation: Template for each forum post whether node or comment.
 *
 * All variables available in node.tpl.php and comment.tpl.php for your theme
 * are available here. In addition, Advanced Forum makes available the following
 * variables:
 *
 * - $top_post: TRUE if we are formatting the main post (ie, not a comment)
 * - $reply_link: Text link / button to reply to topic.
 * - $total_posts: Number of posts in topic (not counting first post).
 * - $new_posts: Number of new posts in topic, and link to first new.
 * - $links_array: Unformatted array of links.
 * - $account: User object of the post author.
 * - $name: User name of post author.
 * - $author_pane: Entire contents of the Author Pane template.
 */
?&gt;

&lt;?php if ($top_post): ?&gt;
  &lt;?php print $topic_header ?&gt;
&lt;?php endif; ?&gt;

&lt;div id="&lt;?php print $post_id; ?&gt;" class="&lt;?php print $classes; ?&gt; ajax-comment-wrapper comment-wrapper-&lt;?php print str_replace('post-','',$post_id); ?&gt;" &lt;?php print $attributes; ?&gt;&gt;
  &lt;div class="forum-post-info clearfix"&gt;
    &lt;div class="forum-posted-on"&gt;
      &lt;?php print $date ?&gt;

      &lt;?php
      // This whole section is for printing the "new" marker. With core comment
      // we just need to check a variable. With Node Comment, we need to do
      // extra work to keep the views caching used for Node Comment from
      // caching the new markers.
      ?&gt;
      &lt;?php if (!$top_post): ?&gt;
        &lt;?php if (!empty($new)): ?&gt;
          &lt;a id="new"&gt;&lt;span class="new"&gt;(&lt;?php print $new ?&gt;)&lt;/span&gt;&lt;/a&gt;
        &lt;?php endif; ?&gt;

        &lt;?php if (!empty($first_new)): ?&gt;
          &lt;?php print $first_new; ?&gt;
        &lt;?php endif; ?&gt;

        &lt;?php if (!empty($new_output)): ?&gt;
          &lt;?php print $new_output; ?&gt;
        &lt;?php endif; ?&gt;
      &lt;?php endif; ?&gt;
    &lt;/div&gt;
    &lt;?php /* End of posted on div. */ ?&gt;

    &lt;?php if (!empty($in_reply_to)): ?&gt;
     &lt;span class="forum-in-reply-to"&gt;&lt;?php print $in_reply_to; ?&gt;&lt;/span&gt;
    &lt;?php endif; ?&gt;

    &lt;?php /* Add a note when a post is unpublished so it doesn't rely on theming. */ ?&gt;
    &lt;?php if (!$node-&gt;status): ?&gt;
      &lt;span class="unpublished-post-note"&gt;&lt;?php print t("Unpublished post") ?&gt;&lt;/span&gt;
    &lt;?php endif; ?&gt;

    &lt;span class="forum-post-number"&gt;&lt;?php print $permalink; ?&gt;&lt;/span&gt;
  &lt;/div&gt; &lt;?php /* End of post info div. */ ?&gt;

  &lt;div class="forum-post-wrapper"&gt;
    &lt;div class="forum-post-panel-sub"&gt;
      &lt;?php if (!empty($author_pane)): ?&gt;
        &lt;?php print $author_pane; ?&gt;
      &lt;?php endif; ?&gt;
    &lt;/div&gt;

    &lt;div class="forum-post-panel-main clearfix"&gt;
      &lt;?php if (!empty($title)): ?&gt;
        &lt;div class="forum-post-title"&gt;
          &lt;?php print $title ?&gt;
        &lt;/div&gt;
      &lt;?php endif; ?&gt;

      &lt;div class="forum-post-content"&gt;
        &lt;?php
          // @codingStandardsIgnoreStart
          // We hide the comments and links now so that we can render them later.
          hide($content['taxonomy_forums']);
          hide($content['comments']);
          hide($content['links']);
          if (!$top_post)
            hide($content['body']);
          print render($content);
          // @codingStandardsIgnoreEnd
        ?&gt;
      &lt;/div&gt;

      &lt;?php if (!empty($post_edited)): ?&gt;
        &lt;div class="post-edited"&gt;
          &lt;?php print $post_edited ?&gt;
        &lt;/div&gt;
      &lt;?php endif; ?&gt;

      &lt;?php if (!empty($signature)): ?&gt;
        &lt;div class="author-signature"&gt;
          &lt;?php print $signature ?&gt;
        &lt;/div&gt;
      &lt;?php endif; ?&gt;
    &lt;/div&gt;
  &lt;/div&gt;
  &lt;?php /* End of post wrapper div. */ ?&gt;

  &lt;div class="forum-post-footer clearfix"&gt;
    &lt;div class="forum-jump-links"&gt;
      &lt;a href="#forum-topic-top" title="&lt;?php print t('Jump to top of page'); ?&gt;" class="af-button-small"&gt;&lt;span&gt;&lt;?php print t("Top"); ?&gt;&lt;/span&gt;&lt;/a&gt;
    &lt;/div&gt;

    &lt;div class="forum-post-links"&gt;
      &lt;?php print render($content['links']); ?&gt;
    &lt;/div&gt;
  &lt;/div&gt;
  &lt;?php /* End of footer div. */ ?&gt;
&lt;/div&gt;
&lt;?php /* End of main wrapping div. */ ?&gt;
&lt;?php print render($content['comments']); ?&gt;


Since the forum post and the 1st comment have the same number 1 you will notice that clicking reply will affect the node post as well. Therefore, you will need to use jQuery to modify or remove the 1 from comment-wrapper-1 of the forum (node) post.