Your unit is behaving very strangely. Even if the iPod wakes itself up immediately when it's shut down the bootloader should load Rockbox, not the Apple firmware. Does the iPod sleep normally from the Apple firmware?
Anyway, it's good to report the (Rockbox) revision number you're using. Then try downloading the current build and verify that it still happens there.
A couple of further questions: When did you install Rockbox? Did this problem begin suddenly?