The AutoRecover feature is not a replacement for manual saving; instead, AutoRecover offers extra security if Word crashes. Each *.asd fil is discarded if Word exits normally.
As far as I know, "Keep the last autosaved version if I close without saving" only applies to unsaved files, that is, files that have never been saved to disk.
MVP Graham Mayor has created an add-in that saves backups; see
http://www.gmayor.com/automatically_backup.htm.