Almost every peace lily i've owned this has happened to. The plant will be fine, then suddenly over the course of a week or more, black spots will appear on a few leaves. It affects old and new leaves. Eventually it spreads to others as well. Cutting off the affected leaves doesn't stop the problem. The spots will appear on other leaves eventually. As you can see the leaf begins to get soft, rather than the usual firm springiness expected.
This particular plant is an offshoot to another that the same thing happened to about a year ago.
I only water the plant with filtered water when it starts to droop and soil is dry. It's in a bright, but indirectly lit space, and the temperature doesn't vary more than 10 degrees per day.
Why does this happen and what can I do about it?