The menu is generated by the function _wp_menu_output. If you look at the place where the links are generated (currently lines 158-162 and 170-174) you see that the admin.php?page= part is omitted under certain circumstances. One of those is an empty $menu_hook.
The variable menu_hook is filled by a call to get_plugin_page_hook, which will return empty if no action is bound to the hook. This translates to: there is no callback function defined to generate the page.
Now let’s look at the hook order: plugins are loaded before themes, so if you generate the submenu before the parent menu (which you do if you initialize the parent menu in the theme’s functions.php) there might be a problem at line 190-192 of add_submenu_page: it might not be possible to bind an action to the hook at that point because the parent page is undefined.
Disclaimer: I analysed the code from the top of my head, so I may have made a mistake there.
Anyway, if you insist on initializing stuff from your functions.php, don’t try to initialize the submenu in your plugin. Instead just define the function in your plugin and call it from the theme as well.