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While growth and dissolution of surface nanobubbles has been widely studied in recent years, their stability under pressure changes or a temperature increase has not received the same level of scrutiny. Here, we present theoretical predictions based on classical theory for pressure and temperature thresholds ($p_c$ and $T_c$) at which unstable growth occurs for the case of air nanobubbles on a solid surface in water. We show that bubbles subjected to pinning have much lower $p_c$ and higher $T_c$ compared to both unpinned and bulk bubbles of similar size, indicating that pinned bubbles can withstand a larger tensile stress (negative pressure) and higher temperatures. The values of $p_c$ and $T_c$ obtained from many-body dissipative particle dynamics (MDPD) simulations of quasi-two-dimensional (quasi-2D) surface nanobubbles are consistent with the theoretical predictions, provided that the lateral expansion during growth is taken into account. This suggests that the modified classical thermodynamic description is valid for pinned bubbles as small as several nanometers. While some discrepancies still exist between our theoretical results and previous experiments, further experimental data is needed before a comprehensive understanding of the stability of surface nanobubbles can be achieved.