The problem is that Outlook is not actually storing the text-only version. However, modern Outlook still retains the MIME headers - and there is a hack to get Outlook to retain the entire message content as well.
The full details are here: About.com - basically you add a new DWord
"SaveAllMIMENotJustHeaders" with value
HKEY_CURRENT_USER\Software\Microsoft\Office\11.0\Outlook\Options\Mail. This superuser answer has more detail, in case the link moves/changes.
Outlook then logs the entire message source where it previously logged just the MIME headers. If you view these headers now (Outlook calls them "Internet headers"), then you should get the full message source. You should be able to find the plain-text version of the email near the top of the source.
Another option, of course, is to set up a text-only email client to read your mail with.