We report results from experimental studies on the current driven breakdown of the quantum Hall effect in an InAs/GaSb-based electron–hole system. We find that the critical currents observed in this system are typically much smaller than those reported for single carrier-type systems. Width dependence measurements show two regimes of behaviour. For sufficiently wide samples, the critical current has a linear dependence on the channel width, while for narrower samples, the critical current has a strong tendency to be vastly reduced. There is a critical width at which this crossover occurs, which is found to depend on the magnetic field, Fermi energy and the ratio between the electron and hole concentrations. We refer to the two regimes as the 'linear regime' and the 'fragile regime'. For samples in the linear regime, critical electric fields or macroscopic critical current densities can be defined. Although the absolute values seem small compared to single carrier-type systems, the values are found to be comparable when scaled by the activation energies. In the fragile regime, the critical current is disproportionately small compared with single carrier-type systems.