What external factor could cause increased current draw?
Static discharge could be causing one of the inputs to the processor (or even an input to another chip) to change state. Look for unterminated inputs, add strong pullups or pulldowns as appropriate, or just add capacitors to the unterminated inputs (something like 0.1uF). I have seen problems like this many times. I have seen units which would power on as a result of static discharge, and I have seen units where reset could be asserted due to static discharge.