Using official Arduino Mega ADK via proper 3.3V level shifter. Powering ENC with 3.3V from the same Arduino.

ENC stopped responding to pings after just one night. The main program continues to work.

The main program polls 1-wire temperature sensor, displays the temperature to an SPI display and controls another device using standard digital outputs.

I strongly suspect that the problem is in Errata 14.

If I have some time (which is not likely to happen any time soon) I'll look into it and will try to fix it for EtherCard library as it is smaller for I will need all that stuff to fit into Pro Mini based on ATmega 328.