PyPI downloads shield showing "rate limited by upstream service"

The PyPI Downloads badge seems to fairly often be showing up like this:

I think for other services the cache time was increased to address the issue.

It might also be nice to have an option to tell shields.io to return a 0 width image in case of an error -- since I'm using it in a place where it would be "nice to have" but if it frequently shows an error message than I'd rather just remove it entirely than make users see an error message.

Start by locating the PyPI Downloads badge and the upstream request and cache handling it uses. Reproduce the rate-limited response, then verify that the badge avoids frequent upstream errors through longer caching; consider the requested zero-width-on-error behavior separately and confirm the resulting image output.

Written by the indexing model from the issue text.