We're human beings, not robots, so we can't really perform a song idenitically every time out. The question is really how much variation is preferable.

As a non-professional "hobbyist" performer working within very loosely-defined "traditions," I can offer some thoughts on my own experience:

As I first begin incorporating a new piece into my "working" repertoire, it'll probably sound quite a bit different each time I perform it, as new shades of meaning come to mind and as various vocal and instrumental "approaches" or techniques are experienced, practiced, and improved.

This process of learning and developing a way to get the song accross can be largely unconscious. Even if I'm trying to do it the exact same way each time, my performance can't help but evolve, for better or for worse. Eventually, the end product "matures," or kind of settles in.

Sometimes, unfortunately, the song's treatment doesn't mature so much as it stagnates ~ falls into a less-than-pleasant rut ~ in which case one has to go back and try changing the approach again.

Some performers are more easily bored than others with their own repetitive renditions. The most obvious example is the ever-controversial Mr Bob "Dylan" Zimmerman, who tries so hard to make even his most familiar songs as unrecognizable as possible. (I realize that the original question specifically referred to traditional songs, whereas The Bob restricts himself mostly to his own compositions, which may or may not fit your definition of "folk music." If you find this reference irrelevant, so be it.)

Another angle:

Working within my own set of skills and limitations as an instrumentalist, I find it impractical to consider changing the way I play a piece, as opposed to how I try to sing it. With a new song, I will try to play it exactly the same way every time, with the result that it (hopefully) improves steadily, albeit very gradually, with time. If I figure out a variation or two, I'll work it into the arrangement ~ play the simple original bit for the first few verses/repetitions, and save the embellished version for later in the performance, the big final climactic go-round or whatever. Over time, as the instrumental part solidifies and strengthens, I usually find myself increasingly able ~ freer ~ to concentrate on the singing and to explore different, more deeply interpretive vocal approaches.