nginx&Wordpressで404のキャッシュが生成されません。

user -> nginx -> apache(Wordpress)
という構成になっています。

200のキャッシュは生成されて問題ないのですが、404のキャッシュは生成されず、常にbackendのapacheをアクセスするようになってしまいます。
なぜ404キャッシュが生成されないのでしょうか？

設定は以下のようになっています。

/etc/nginx/nginx.conf

user              nginx nginx;
worker_processes  2;
worker_rlimit_nofile 10240;

error_log  /var/log/nginx/error.log warn;

pid        /var/run/nginx.pid;

events {
    worker_connections  8192;
    use epoll;
}


http {
    include       /etc/nginx/mime.types;
    default_type  application/octet-stream;

    log_format  main  '$remote_addr - $remote_user [$time_local] "$request" '
                      '$status $body_bytes_sent "$http_referer" '
                      '"$http_user_agent" "$http_x_forwarded_for"';

    access_log  /var/log/nginx/access.log  main;

    server_name_in_redirect off;
    server_tokens      off;

    sendfile           on;
    tcp_nopush         off;

    keepalive_timeout  5;

    client_max_body_size    4M;
    client_body_buffer_size 256k;

    if_modified_since before;

    gzip              on;
    gzip_http_version 1.0;
    gzip_vary         on;
    gzip_comp_level   6;
    gzip_types        text/plain
                      text/xml
                      text/css
                      text/javascript
                      application/xhtml+xml
                      application/xml
                      application/rss+xml
                      application/atom_xml
                      application/javascript
                      application/x-javascript
                      application/x-httpd-php;
    gzip_disable      "MSIE [1-6]\.";


    # proxy cache
    proxy_cache_path  /var/cache/nginx/proxy_cache levels=1:2
                      keys_zone=czone:32m max_size=256m inactive=1440m;
    proxy_temp_path   /var/cache/nginx/proxy_temp;
    proxy_cache_key   "$scheme://$host$request_uri";
    proxy_set_header  Host               $host;
    proxy_set_header  X-Real-IP          $remote_addr;
    proxy_set_header  Remote-Addr        $remote_addr;
    proxy_set_header  X-Forwarded-Host   $host;
    proxy_set_header  X-Forwarded-Server $host;
    proxy_set_header  X-Forwarded-For    $proxy_add_x_forwarded_for;
    proxy_set_header  X-Forwarded-Proto  $scheme;
    proxy_set_header  X-UA-Detect        $mobile;
    proxy_set_header  Accept-Encoding    "";
    proxy_hide_header X-Pingback;
    proxy_hide_header Link;
    proxy_hide_header ETag;
    proxy_connect_timeout 5;
    proxy_send_timeout 10;
proxy_read_timeout 90;
    proxy_cache_use_stale timeout invalid_header http_500 http_502 http_503 http_504;
    proxy_cache_lock on;
    proxy_cache_lock_timeout 5s;
    proxy_buffers 8 32k;
    proxy_buffer_size 64k;

    include /etc/nginx/conf.d/*.conf;

}

/etc/nginx/conf.d/default.conf

limit_req_zone $binary_remote_addr zone=one:10m rate=50r/s;
limit_req_log_level info;

upstream backend {
    server xxx.xxx.xxx.xxx:8080;
}
server {
    listen       80 default;
    server_name  example.com;
    index       index.html index.htm;
    charset     utf-8;

    access_log  /var/log/nginx/example.com.access.log  main;
    error_log   /var/log/nginx/example.com.error.log;

    set $mobile '';
    include /etc/nginx/mobile-detect;

    set $do_not_cache 0;
    if ($http_cookie ~* "comment_author_|wordpress_(?!test_cookie)|wp-postpass_" ) {
        set $do_not_cache 1;
    }
    if ($request_method != GET) {
        set $do_not_cache 1;
    }


    location / {
        limit_req zone=one;
        proxy_no_cache     $do_not_cache;
        proxy_cache_bypass $do_not_cache;

        proxy_redirect     off;
        proxy_cache czone;
        proxy_cache_key "$scheme://$host$request_uri$mobile";
        proxy_cache_valid  200 6h;
        proxy_cache_valid  404 20m;
        proxy_pass http://backend;
    }

    error_page  502 503 504  /50x.html;
    location = /50x.html {
        root   /usr/share/nginx/html;
    }
}