A rigorous, thermal-capillary model, developed to couple heat transfer, melt convection and capillary physics, is employed to assess stability limits of the HRG system for growing silicon ribbons. Extending the prior understanding of this process put forth by Daggolu et al. [Thermal-capillary analysis of the horizontal ribbon growth of silicon crystals, Journal of Crystal Growth 355 (2012)129-139], model results presented here identify additional failure mechanisms, including the bridging of crystal onto crucible, the spilling of melt from the crucible, and the undercooling of melt at the ribbon tip, that are consistent with prior experimental observations. Changes in pull rate, pull angle, melt height, and other parameters are shown to give rise to limits, indicating that only narrow operating windows exist in multi-dimensional parameter space for stable growth conditions that circumvent these failure mechanisms. (C) 2012 Elsevier B.V. All rights reserved.