Both teenage daughters have new Mini IPods.  When connected to the
computer port, the message "Do Not Disconnect" never goes off.  Even
after charging  for several hours and the meter indicates charging is
complete.  In spite of the warning, we will disconnect after several
hours and everything works OK.  I assumed the caution message would go
off when charging was complete

When connecting an iPod to a computer, it is basically doing two things:

1)Charging the iPod
2)Creating a data connection between the computer and iPod

The message of which you speak is there as you don't interfere with
the data connection the iPod and the computer are having.

While you are not actually transferring any files, you would still be
best to "eject" the iPod before unplugging.  On the PC, just right
click the iPod drive in the My Computer window and it will allow the
iPod to be unplugged safely.  If connected to an Apple, just go to the
Desktop and select the iPod logo and disconnect it.

Another option is to charge the iPod from the wall with the included
adapter.  In this scenario, it won't give the "Do Not Disconnect"
message at all.