Approximate Bayesian computation (ABC) is rapidly gaining popularity in population genetics. One example, msBayes, infers the distribution of divergence times among pairs of taxa, allowing phylogeographers to test hypotheses about historical causes of diversification in co-distributed groups of organisms. Using msBayes, we infer the distribution of divergence times among 22 pairs of populations of vertebrates distributed across the Philippine Archipelago. Our objective was to test whether sea-level oscillations during the Pleistocene caused diversification across the islands. To guide interpretation of our results, we perform a suite of simulation-based power analyses. Our empirical results strongly support a recent simultaneous divergence event for all 22 taxon pairs, consistent with the prediction of the Pleistocene-driven diversification hypothesis. However, our empirical estimates are sensitive to changes in prior distributions, and our simulations reveal low power of the method to detect random variation in divergence times and bias toward supporting clustered divergences. Our results demonstrate that analyses exploring power and prior sensitivity should accompany ABC model selection inferences. The problems we identify are potentially mitigable with uniform priors over divergence models (rather than classes of models) and more flexible prior distributions on demographic and divergence-time parameters.