Codex’s Adding Aside problem for single pages

I’m trying to find a workaround for this problem myself. It happens because the asides are in a loop; on a single page, the loop only displays that one particular post (same thing goes for categories and archives- they will only display posts which match the page specified).

EDIT: Meanwhile, the wordpress miniblog plugin (https://www.nmyworld.com/wordpress/2005/03/miniblog-plugin-01-for-wordpress-15-58/) works fairly well and displays on all pages.