Further complicating matters: Style guides sometimes disagree with dictionaries and each other. So in a publication that defers to a style guide, as most newspapers do, you may see Presidents Day with no apostrophe. But in books, which usually follow a different style guide, you'll probably see Presidents' Day with an apostrophe.
So how then did I answer Mary's question about Founders/Founders' Day? With a loud and resounding "I don't know."
All my attempts to come up with a clear answer failed. First I checked Webster's New World College Dictionary, which is the default dictionary for many newspaper publishers. No listing. Then I checked Merriam-Webster's Collegiate, which is the choice of book publishers. Nothing. I checked the Associated Press Stylebook and the Chicago Manual of Style, neither had it. I even checked two usage guides, Garner's Modern American Usage and Merriam-Webster's Dictionary of English Usage. None of them had a word to say about it.