Peace lilies seem to be sensitive to chemicals in water. Are you using chlorinated city water? I was pleasantly surprised when I moved from the city to the country and switched to well water, because many of my tropicals improved immensely. I've worked in offices where people brought their plants in because the water at their home wasn't as good as the water in a different water district.
I use straight well water on my plants, not the water that goes through the water softener. Each well is different, of course, but chemicals or minerals in the water could be the source of your problem.
