I've seen AWS not actually bill me, and just send email accounts, for months and months. It's not worth their time billing a few cents or even a few dollars a month, so by the time an account "goes wrong" it can have been half a year or more since your card got re-issued, and you've forgotten you need to update Amazon for anything.

(it's much less of an issue if you're piggybacking your AWS stuff on a regularly used Amazon account/creditcard, but if you set this up as a one-off for a tiny S3/CloudFront "web hosting" setup, it could easily bite you on the ass in a few years time...)