If changing my cat's drinking water from tap to distilled for a month and adding some Iodine produces fatigue/behavioral differences in my cat, then it's reasonable to examine what it is about distilled water and/or Iodine that might be affecting her.
That includes the possibility she isn't getting the minerals that she needs from other sources and is reacting to what she was no longer getting from tap.
Consider that deer and other animals crave salt to the point where we put out salt licks for them out in the woods to satisfy their cravings.
It's quite possible that my cat isn't getting enough salt now that she isn't drinking the tap.