We report the phase space defined by the quantum Hall effect breakdown in polymer gated epitaxial graphene on SiC (SiC/G) as a function of temperature, current, carrier density, and magnetic fields up to 30 T. At 2 K, breakdown currents (I_c) almost 2 orders of magnitude greater than in GaAs devices are observed. The phase boundary of the dissipationless state (ρ_xx=0) shows a [1-(T/T_c)²] dependence and persists up to T_c>45  K at 29 T. With magnetic field I_c was found to increase ∝B^3/2 and T_c∝B². As the Fermi energy approaches the Dirac point, the ν=2 quantized Hall plateau appears continuously from fields as low as 1 T up to at least 19 T due to a strong magnetic field dependence of the carrier density.