A power-law like acceleration of seismic moment release (AMR) has been proposed as a precursor to large earthquakes. Because of problems with real-world data, we have used a synthetic seismicity model of 256 interacting faults embedded in a 3-D elastic half-space to search for periods of AMR preceding the largest events (Mw ~ 7.1). In only 5 of 18 cases does the AMR model fit the data significantly better than a linear moment release, and then only weakly so. This proportion, or higher, occurs in 8% of 1000 randomized catalogs. We conclude that either AMR is unlikely to be a common precursor, or that factors contributing to the AMR pattern in the real world are missing from the synthetic model.