Cyclic dominance of species has been identified as a potential mechanism
to maintain biodiversity (see e.g. B. Kirkup and M. A. Riley, Nature 2004).
We address this issue in an illustrative three-species system, being generic
for a broader class of models. While the deterministic approach predicts 
coexistence in the form of neutrally stable oscillations in the population densities, 
we show that fluctuations arising in finite populations drastically alter this picture. 
In particular, after long enough time, two of the three species die out. 
We present a stochastic description to quantitatively underpin our findings.