You can however force it to ignore the cache by manually store your site again:
https://web.archive.org/save/[YOURSITE]
for example:
https://web.archive.org/save/http://blathering.de
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]