Custom Metabox Not Saving

When you do that include, you are trying to add the save_post hook inside the add_meta_boxes_$post_type hook. It should be independent.

add_action( 'add_meta_boxes_page','load_home_meta' );
add_action( 'save_post', 'save_home_meta' );

// Declare all callback functions

Also, you shouldn’t declare a function inside a function. Maybe you should consider creating a plugin for handling this, see: Where to put my code: plugin or functions.php?.
Or, if you really want it inside your theme’s functions.php, do a include for all this meta box code.

You’ll find plenty of working examples here, check this search query:
+save_post +add_meta_box is:answer