Gamma-Ray Bursts (GRBs) are characterized at high energies in their prompt emission by impulsive peaks with sharp rises, often highly structured, and easily distinguishable against instrumental backgrounds. The longer-lived afterglow radiation seen at lower energies is much smoother and would be difficult to detect in a background-limited instrument such as the Gamma-ray Burst Monitor (GBM) onboard Fermi. Observations above 100 MeV of this type of long-lived emission from bright GBM-detected GRBs by the Fermi Large Area Telescope (LAT) suggest the possibility of extended lower-energy gamma-ray emission. We report the results of a search for such emission in GBM GRBs from the first 4 years of operation.