Hello Eugene,
Hope you are doing well. The mailbox interrupt can wake up if the core is in sleep mode, however not from power down, deep power down or deep sleep.
If you would like to wake up from power down you can consider the following:
• Using a reset from the RESET pin.
All wake-up events (other than reset) must be enabled via the power API.
• Using a wake-up signal from any of the serial peripherals in Flexcomm3.
• Using the analog comparator.
• GPIO group interrupt signal.
• RTC alarm signal or wake-up signal.
• OS Event Timer.
To test different wake up signals with the different power modes. I'd recommend to use our lpc_power_management example from our SDK.
Best Regards,
Sabina