Arduino DUE deadlock problem, watchdog not working
Found people suffering with the same problem on Arduino's official forum. It turned out that the problem arises from the schematic of Arduino Due, that fails to hold 'reset' pin high for long enough period of time on power-on.

There are multiple solutions involving adding some capacitance between reset pin and ground pin, but this might damage circuit in long run (at power-off), so I managed to find other way around it: there is an ATmega16U2 used as USE-to-TLL serial chip that have access to reset pin of AT91SAM3X8E.

The ATmega16u2 can be reprogrammed so that on power-on it provide short "HIGH" period to AT91SAM3X8E reset pin. The program for ATmega16U2 can be found here: 
https://forum.arduino.cc/index.php?action=dlattach;topic=167492.0;attach=52901

The updating precision is given here:
https://www.arduino.cc/en/Hacking/Upgrading16U2Due

I've performed the given precision using Arduino UNO as programmer and can confirm that it worked properly.The problem's gone now.