iPod ipod 6th G - battery drains even with new firmware

We have a hand me down 6th gen ipod nano.
It has the latest 1.1 firmware update for the battery turn off feature.

When we press & hold the sleep button,
we get the rotating icon and the ipod nano 6th G powers off.
When we press it again... after waiting several minutes,
it displays the Apple logo and then boots to the main screen.

Our problem seems to be that the battery drains to nothing,
EVEN with the ipod nano 6th G turned off with the rotating icon from 1.1 firmware update.

We can fully charge it - take it off the charger - full battery is displayed,
and the press/hold the sleep to get the rotating icon.
The next day, the battery is dead !!

I even had the battery replaced - but nothing has changed...

Would just like to hear from other ipod nano 6th gen users about their experience....

1 - when you press the sleep button with firmware 1.1,
do you get the rotating gear wheel ?

2 - does this really turn it completely off ?

3 - after a complete & full charge and turning it "off",
if you turn it on the next day,
how's the battery - ok or dead ?