Leprechaun,
First, it's possible that your current sound driver doesn't support the process. I recommend finding, then downloading and installing a current driver for your sound card. (In order to do that, RIGHT click on "My Computer", choose "Properties", click on the "Hardware" tab, then click on the "Device Manager" button. When that loads, click on the + sign next to "Sound, Video, and Game Controllers" to display the specific devices there. RIGHT click on the specific sound device listing, choose "Properties", then click on the "Driver" tab.) Write down the manufacturer/provider, driver date and driver version. If you have a brand name computer, you can visit the manufacturer's website and find a current sound card driver. If nothing else, you should be able to visit the sound card manufacturer's website and download their updated driver.
Another important note, the "Sound Recorder" program is relatively limited for recording sound. (Usually only up to 60 seconds worth of recording time.) The link below for the "FreeCorder" program allows you to record much longer sound recordings and should allow you to record any sound that would travel through the speakers such as your "Stereo Mix" method. Like it's name suggests, it's FREE. I recommend installing Freecorder, then trying again.
http://www.freecorder.com/
Hope this helps.
Grif