I also had this same issue on a site I was working on. Determined that SSL would resolve pages correctly with permalinks off.
SOLUTION::
Add rewrite rules to SSL configuration under the <Directory> tag inside the SSL VirtualHost definition.
Hope this is helpful ??
Example:
<Directory /var/www/sites/example.com/public_html>
AllowOverride none
Order Allow,Deny
Allow from all
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ – [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</Directory>