However, if those PDFs are requested via HTTP, unless the bank gives appropriate caching headers I think Chrome is technically correct in re-requesting them: they might have changed in the meantime. (I assume it does the same with webpages when you save them.)
The fact that the bank gives you a URL you can only HTTP GET once does sound like very bad implementation on their behalf. Perhaps it's a cookie issue, or even a bug in Chrome itself?
Here is one example: You opened the front page of some news site a few hours ago and now want to save it. Since news sites change frequently you would save a completely different page compared to what you actually wanted to save if the page were re-requested when saving. This is destructive behavior! No browser should do that.
(I just tested what Google Chrome actually does. It does not actually re-request the page when saving.)