First of all, there are many folk songs which did not last.
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I believe that the songs which did last have two characteristics: good melody and good rhyme. Melody is indefinable, but when I think about it, I guess you could define it as that which makes a sequence of notes memorable.

And it is amazing the way rhyme makes words easy to remember. Consider the baloney that people perpetuate (such as "no pain, no gain") merely because the words rhyme.