First of all, a big thank you to Kelly for letting me make a copy of her site so I could diagnose this issue.
Kelly:
First, the reason why your first link doesn’t show images and the second does is because the first is a list of sub-categories and the second is a list of posts. So they use different code.
Second, this is not a problem with the plugin. It’s a problem with the code being used in your custom category.php to pull the image from the database. You can read about it here:
https://www.studiopress.com/important-announcement-for-genesis-plugin-developers
but the short version is that as of genesis 2.3.0, $term->meta is no longer populated. This line is causing the problem:
$image = isset($term->meta['term_thumbnail_id']) ? wp_get_attachment_image($term->meta['term_thumbnail_id']) : '<img src="/wp-content/plugins/genesis-taxonomy-images/assets/images/placeholder.png" />';
So you’ll need to get that fixed by whoever wrote the custom code for you, if it’s not you that wrote it. You can either do it directly or by using the function called gtaxi_get_taxonomy_image()
which is in the plugin for just this purpose.