As you might know: the wayback machine from archive.org saves snapshots of websites. It does this automatically or can be forced to do so. However. If you ever had a 301 redirect on your site you are very much doomed.
Like browsers also the wayback-machine caches the redirect and does not continue to take snapshots from your sites. Even if you enter your url into the wayback-machine, you still will be redirected.
You can however force it to ignore the cache by manually store your site again:
Et voílà: Everything works nice from now on.
[Image is CC-BY-NC-ND © David Baldingerhttp://www.dbaldinger.com/opinion_cartoons/second_page/wayback.html]