When a piece of new/experimental/avant-garde/contemporary (etc.) music gets its first performance, chances are high that it will also be the last performance. In itself, this is neither a good or bad thing; while in some cases, the lack of repeat performances is definitely regrettable, in other — perhaps most — cases, it is no great loss, and in still others, the ephemeral nature of the event is actually a design feature.
Accepting the single performance can be a practical and economic decision. The supply of new musical works is large and the time and resources for proper audition are severely limited. But there can be an aesthetic, even metaphysical dimension to a decision to consciously limit the realization of a musical idea to a one-off occasion. The legendary ONCE Festival (in at least one version of the legend) perhaps put this idea in the air first. I think Philip Corner's score ONE NOTE ONCE found the condensed, koanic, essence of the idea. (Jean Tinguely's self-destructing sculptures are extreme examples of the idea in another medium.)
I think, however, a decision to affirm the transitory in a piece is a natural extension of the ephemeral character of the materials of music, the sounds themselves, dissipating, or as Marx and Engels had it, melting into air.
A finished score is often only a single instance or realization of a musical idea or process, a one-off performance in the domain of composition. The decision to accept a single result over a plurality might be characterized in music-historical terms as a decision to avoid the creation of repertoire, or maybe it's just a sensible act in an age of mechanical (and electronic) reproduction. (As someone noted, the great lesson of mass reproduction is that we don't want everything to be the same, or you'd never find your own car in a parking lot.)
What interest might there be in taking a process-based piece like Steve Reich's Piano Phase, and using an alternative set of pitches to those Reich himself chose? How dependent on that diatonic-but-not-necessarily-tonal configuration chosen by Reich is the identity of that piece? Idea, instance, identity. Is it interesting or relevant that John Cage used the same methods and materials designed for Music of Changes to compose the miniatures of Seven Haiku, or (in at least one version of the story) the temporal structure of 4'33"? Are these new pieces or just left-overs? (Any composer who cooks knows the value of left-overs.)
A composer I admire very much, Andrew Culver, assisted John Cage for many years and part of his work involved writing small computer programs to answer, through chance operations (or, more precisely, effective simulations of the same) questions which Cage had assigned to such decision-making processes in his pieces. When Cage died, Culver had the tools require to generate an unlimited number of new works using Cage's own algorithms. But Culver did not do this, recognizing that Cage himself had the same possibility but had always accepted a single realization of a score. (This is not to discount the fact that Cage did, indeed, often use a lot of trial and error in adjusting his questions until they yielded the broad kinds of results which interested him. Walter Zimmermann's analysis of Quartets I-VIII in the Anarchic Harmony volume describes an example of this working process.)
Recently, when working with some young people, we spent some time with the score and realization of Cage's Williams Mix. An astonishing piece involving a plethora of source sound recordings and a hugely difficult-to-realize score requiring thousands of tape splices in wildly variable but breathtakingly precise dimensions and orientations. I don't know if there have been subsequent realizations of the piece to that made by Cage and colleagues in 1952/53, but Cage, with the publication of the score, explicitly suggests the possibility of new realizations. And now, it seems eminently realizable, in real time, as live computer music, with the computer randomly (or, more precisely, an approximation of randomly) selecting out and processing slices of sounds extracted from a stored library. An indefinite number of new realization could be made, but in doing so, are we learning or experiencing anything substantially different from that original realization?