Karl Popper's argument that deductive logic and falsifiable hypotheses are necessary for the growth of scientific knowledge has been controversial. One approach to assess the relevance of his ideas to medical science has been to evaluate examples of successful research. Another approach is to analyze an unsuccessful investigation. The inconclusive search for a unique 'chronic fatigue syndrome' offers a well-documented case-study for this analysis. Over the past 130 years, numerous studies have provided clinical and epidemiological data, which have supported competing hypotheses about the etiology of chronic fatigue. However, few hypotheses have been refuted because it has not been possible to establish objective standards of inquiry for a subjective symptom like fatigue. As a result, intensive research efforts have not converged on correct explanations by eliminating erroneous ideas. This unsuccessful investigation illustrates how non-falsifiable hypotheses are insufficient to advance medical knowledge, even when there is an abundance of empirical data.