Hi Ray,
These are generally known as favicons.ico (Favorite Icons) and they normally
will only last until your Internet Explorer Temp files are cleared.
This program will allow you to save the favicons.ico (Favorite Icons)
permanently in a different folder and re-associate your favorites with the
stored icons.
FavOrg - Restore and Save Favorite Icons (Line 108)
http://www.kellys-korner-xp.com/xp_tweaks.htm
Workaround:
Navigate to the Temporary Internet Files, and drag the icons to the desktop
and rename them to whatever name you like.
Create a folder called Icon Selection. Move all of the renamed favicons to
this folder placed in the root directory of C. Right click on the Icon,
select Browse and navigate to your Icon Selection folder. Choose the
renamed favicon and click ok. These icons will be permanent.