Why will comments not remain open on custom post types?

Question

I have a WP install which makes use of default posts and of one custom post type (reviews). Discussion settings allow comments on both these post types. The comment form is present when viewing posts but I am getting "comments are closed" on the CPTs front-end.

If I edit the individual reviews I can see that "Allow comments" is not checked. If I check this and hit "Update" it reverts to unchecked (this doesn't happen with "Allow trackbacks and pingbacks").

This unchecking also happens if I "Quick Edit" in the All Reviews admin page too.

Comments which are already in the database are still visible using comments_template();, but the form will not appear on CPTs because comments cannot be enabled.

I have made sure that "Admin > Settings > Discussion > Allow people to submit comments on new posts" is checked. I have unchecked/rechecked it as per this question but it has made no difference.

The CPT is declared in functions.php as follows:

add_action('init', 'all_custom_post_types');

function all_custom_post_types() {
    $types = array(
        array(
            'the_type' => 'review',
            'single' => 'Review',
            'plural' => 'Reviews'
        ),
    );

foreach ($types as $type) {
    $the_type = $type['the_type'];
        $single = $type['single'];
        $plural = $type['plural'];
        $labels = array(
            'name' => _x($plural, 'post type general name'),
            'singular_name' => _x($single, 'post type singular name'),
            'add_new' => _x('Add New', $single),
            'add_new_item' => __('Add New '. $single),
            'edit_item' => __('Edit '.$single),
            'new_item' => __('New '.$single),
            'view_item' => __('View '.$single),
            'search_items' => __('Search '.$plural),
            'not_found' =>  __('No '.$plural.' found'),
            'not_found_in_trash' => __('No '.$plural.' found in Trash'),
            'parent_item_colon' => '',
        );
        $args = array(
            'labels' => $labels,
            'public' => true,
            'publicly_queryable' => true,
            'show_ui' => true,
            'query_var' => true,
            'rewrite' => true,
            'capability_type' => 'post',
            'hierarchical' => true,
            'has_archive' => true,
            'menu_position' => 5,
            'supports' => array('title','editor','thumbnail','comments'),
            'show_in_menu' => true,
            'show_in_nav_menus' => true,
            'taxonomies' => array('category','post_tag'),
        );
        register_post_type($the_type, $args);
    }
}

comments are included under supports in the $args here.

Why would this be happening and how can I fix it?

EDIT

I have fixed this by registering another CPT and using that instead. The comments issue is only affecting the posts with the specific type of review. I'm not posting this as an answer because to my mind it is a workaround and not a solution.

Presumably something got logged somewhere (in the database?) and I haven't been able to find or flush it. I'd still be interested in what this might be and how I could have avoided it.