I have encountered the concept of eternal return e.g. in reading about Friedrich Nietzsche (1844 – 1900) and Pythagoras (c. 570 – c. 495 BC). This is one formulation from Nietzsche's The Will To Power:
If the world may be thought of as a certain definite quantity of force and as a certain definite number of centers of force - and every other representation remains indefinite and therefore useless - it follows that, in the great dice game of existence, it must pass through a calculable number of combinations. In infinite time, every possible combination would at some time or another be realized; more: it would be realized an infinite number of times. And since between every combination and its next recurrence all other possible combinations would have to take place, and each of these combinations conditions the entire sequence of combinations in the same series, a circular movement of absolutely identical series is thus demonstrated: the world as a circular movement that has already repeated itself infinitely often and plays its game ad infinitum.
I have noticed that the Wikipedia article on eternal return cites only a single (brief) argument against eternal return in Georg Simmel's (1858 – 1918) formulation: he seems to be arguing that time may run into "local loops", so not everything is bound to repeat infinitely often. But more than this counter-attempt must have accumulated during the concept's long history (also in Eastern philosophy).
What (substantially) other argument's have philosopher's (and others) put forward against the concept of eternal return? What is seen as its main fallacy and can account for the fact that it is (apparently) absent from contemporary discourse.