I asked the developer of qBittorrent about this, and he told me to come here instead.
I've been using the portable qBittorrent for 2 or 3 versions now, and in none of those versions has the Auto-Shutdown function worked for me. When I set the program to auto-close upon completion of the downloads, nothing happens. The same is true when I set it to shutdown the PC.
Is this something intentionally disabled in the PA version, or is it a bug?