So, the apache logs show nothing untoward that might cause the issue during that time period (posted above).
The forum error logs are also not indicating any exceptions that might cause the issue.
We're running SMF 2.0.12 (current) on PHP 5.6.27. The Sessions support is via files in /tmp (standard config for shared hosting).
All I can think of so far is something did a cleanup of the /tmp directory and removed the sessions files so there was no webserver-based info about prior sessions. I'll look at the SMF code for 'action=unread' processing and see what I find.
It still remains a mystery as to the root cause...