Hmmm...could we say maybe that a song becomes a folk song when it loses its identification with an individual songwriter and becomes part of the culture and tradition and history of a community? I think that's where a song starts to become "folk" - when it moves from individuals to a community. If it is truly a "folk" song, it should express the character of the community from which it springs.
That's only the start, though. I think it's a slow evolution. Most songs don't become "folk" until they've gone through many changes. If there's only one form of a song, maybe it isn't really a folk song.
Thirdly, I think a folk song should have a certain timelessness. It should express both the past and the current character of a community. If it is no longer relevant to a community, perhaps it it becomes an artifact, and not a true folk song.
That, in three paragraphs, is my less-than-humble opinion.
-Joe Offer-