Hi,
I suppose that you can connect a large bypass capacitor on the 3.3V power supply pins, the LPC1857 has BOD, which can detect the power supply voltage, when the voltage is less than a threshold which is programmable, the BOD will fire an interrupt, in the BOD ISR, you can write the important data to on-chip EEPROM or flash. Because large capacitor is connected, it can keep a long time so that the data can be written reliably.
BR
XiangJun Rong