Solution found; posting info for anyone that may stumble upon this in the future.
.htaccess was recently deleted and rebuilt by re-saving permalink settings. The HTTPS Redirect plugin settings had to also be re-saved in order to rebuild the .htaccess code that handles HTTPS redirection.
Update:
- Cleared browser cache and tried again; same problem.
Also, I noticed on pages that DO recognize that the user is logged in, the following cookies exist:
wordpress_logged_in_[hash]
wordpress_sec_[hash]
wp_postpass_[hash]
On pages that DO NOT recognize the user as logged in, the wordpress_sec_[hash] cookie disappears.
