Curious if the content on those sites might have high value to Google? Such as if they have data that is new or unavailable elsewhere, or if they're just standard sites, and you've just been unlucky?

I have had odd bot behavior from some major crawlers, but never from Google. I wonder if there is a correlation to usefulness of content, or if certain sites get stuck in a software bug (or some other strange behavior).

Google do value the sites, they have data unavailable elsewhere. At some point we had an automated message saying the site had too many pages and would no longer be indexed, then a human message saying that was a mistake, and our site was an exception to that rule.

But as with any contact with these large companies, our contact eventually disappeared.