[Answered ]-How do I use a virtualenv-based deployment method without upgrading to each and every upstream version?

First, this is an unusual situation. I’ve never seen another package remove all old releases the way BeautifulSoup does. I consider that rather user-hostile behavior, except perhaps in cases of a serious security fix.

That said, if you want a reliable build process using pip, you really need to mirror all the packages you rely on locally. It’s not hard to do; you can use pip’s –download option (or your existing pip cache) to get all the package tarballs, then just dump them in an indexed, web-served directory and use –find-links in your requirements file to point pip there (plus –no-index to tell it not to use PyPI).