When turning on an iPod, there's the Apple screen before Rockbox loads. The low battery shutdown happens even before the Apple screen, so it can't be due to the Rockbox bootloader.
The behaviour may be by design rather than due to a bug. When running the Apple firmware, the iPod only shuts down when it detects low battery. Otherwise, it sleeps or hibernates. The battery level for turning on from an off state may be set higher to prevent people from repeatedly turning on an iPod when it shuts down from low battery.
I have noticed more of that behaviour while my 5G iPod is cold and/or at a lower state of charge, so it definitely seems related to a measurement of battery voltage. Maybe you're seeing it more recently because it's colder?