Thank you for the replies. They give me more hope because I was thinking along similar lines.
I certainly plan on reaching out to the authors of old articles that lost link, but I am not so sure sometimes. One of the old websites specifically got its coverage from being controversial so I am not sure if they unlinked due to it being down or due to complaints from people pointing out how they were helping it by linking to it. I have been noticing articles like https://moz.com/learn/seo/backlinks and I would hate to risk losing mentions on high quality sites by drawing attention to new editors that might just delete the articles entirely.
Another question I have related to mentions is mentions in books. I have noticed a site of mine showing up in Google Books from a couple of published books discussing it. Does that help SEO like a brand mention on a high quality site?
I would think that Google would consider sites mentioned in published books to be more authoritative than ones just mentioned in blogs or news stories.