Nano vs Mini - Sleep not working the same way

Hey folks,

I am working on a project using an AVR and the RF24 module for a wireless sensor module.
The code is quite large already, so I am posting just the code of the function at the moment.

void NodeConfig::putNodeToSleep(uint16_t sleepPeriod) const
{
    IF_DEBUG(printf_P(PSTR("** Sleeping for %u seconds.."), sleepPeriod));
    //attachInterrupt(digitalPinToInterrupt(2), wakeUpNode, CHANGE);
    delay(STATE_DELAY);
    bool keepSleeping = true;
    unsigned int sleepLeft = sleepPeriod;
   
    while (keepSleeping)
    {
        delay(STATE_DELAY);
        if (sleepLeft > RF24_MAX_SLEEP)
        {
            sleepLeft -= RF24_MAX_SLEEP;
            keepSleeping = network.sleepNode(RF24_MAX_SLEEP, 0, 0);
            IF_DEBUG(printf_P(PSTR(". %u left"), sleepLeft));
            IF_DEBUG(Serial.println(keepSleeping ? 't' : 'i'));
        }
        else
        {
            keepSleeping = false;
            network.sleepNode(sleepLeft, 0, 0);
        }
    }
    IF_DEBUG(printf_P(PSTR(" waking up **\n")));
    detachInterrupt(0);
}

First: So far we have used a Arduino Nano as development platform, because the attached USB port made it easier. The software is working, collecting data, and - most importantly - the Sleep is working as expected. (collect and send data, sleep for 3minutes, repeat)

So, now we are moving to the Mini (to reduce power consumption), and the same code is put on the Mini Pro, but now the Mini never goes to sleep. It just keep sending data roughly every second.

So, I am wondering now - since both have the same ATmega328p on it - I was expecting that both would behave the same way.
Looking at the schematics of the two boards did not reveal any clue so far.

Thus, I am here to ask if there are any "hidden" differences between the two boards (Nano vs Mini)?
Or is perhaps someone can give me a clue, why these two would not behave the same way if they were flashed with the same code.

Thanks in advance for any advice.

PS: We first put the bootloader on the mini using an USBtinyISP, the firmware is then flashed using a serial adapter.