I guess it's a combination of the attach/detachInterrupt calls and the wrong sleeping mode. According to the datasheet edge detection of external interrupts needs the I/O clock which is not available in power down sleep. Only a level trigger can wake the processor from power down state. This would mean the processor wakes from the powerdown sleep only by the watchdog interrupt which is set to 8s in the code we saw. So either the code posted yet is not the one used for test with the signal posted in answer #11 or the processor doesn't act exactly as the datasheet describes when edge triggered interrupts are configured and a power down sleep is scheduled.
Have you tried the sketch without the sleep code and the detach/attach calls?
BTW: Why are you setting the pin to INPUT_PULLUP? In my understanding of your external circuit the interrupts gets a clear LOW/HIGH signal. Am I wrong?