We report experimental results on the breakdown of the low-dissipation currents in the integral quantum Hall effect at temperatures from 6 to 0. 5K, and in magnetic fields up to 28T using Corbino-ring geometry. The Hall current at which the abrupt breakdown occurs is the same for the center of the i equals 1, 2, and 4 resistance minima. The critical current decreases rapidly away from this central position. We discuss three possible models to explain our observations.