Owing to the high stored energy of ITER plasmas, the heat pulses due to uncontrolled Type I edge localized modes (ELMs) can be sufficient to melt the top surface of several poloidal rows of tungsten monoblocks in the divertor strike point regions. Coupled with the melt motion associated with tungsten in the strong tokamak magnetic fields, the resulting surface damage after even a comparatively small number of such repetitive transients may have a significant impact on long-term stationary power handling capability. The permissible numbers set important boundaries on operation and on the performance required from the plasma control system. Modelling is carried out with the recently updated MEMENTO melt dynamics code, which is tailored to tackle melt motion problems characterized by a vast spatio-temporal scale separation. The crucial role of coupling between surface deformation and shallow angle heat loading in aggravating melt damage is highlighted. As a consequence, the allowable operational space in terms of ELM-induced transient heat loads is history-dependent and once deformation has occurred, weaker heat loads, incapable of melting a pristine surface, can further extend the damage.