I recently upgrade to WordPress 3.4.1. Now I encounter a WordPress generated 404 error page whenever I try to access a child page from the frontend.
I went through all my plugins and deactivated them. Deactivating WordPress HTTPS fixed the problem (using version 3.1.1 of the plugin).
With that plugin activated, disabling custom permalinks also fixed the problem. I would like to leave the permalinks intact if possible.
I switched over to the Twenty Eleven theme. The problem still existed, so I switched back to my custom theme.
The child pages give 404s whether or not the pages are designated HTTPS secured, and whether or not the parent is designated HTTPS secured.