High-conductivity solid electrolytes, such as the Na superionic conductor, NaSICON, are poised to play an increasingly important role in safe, reliable battery-based energy storage, enabling advanced sodium-based batteries. Coupled demands of increased current density (≥0.1 A cm–2) and low-temperature (<200 °C) operation, combined with increased discharge times for long-duration storage (>12 h), challenge the limitations of solid electrolytes. Here, we explore the penetration of molten sodium into NaSICON at high current densities. Previous studies of β″-alumina proposed that Poiseuille pressure-driven cracking (mode I) and recombination of ions and electrons within the solid electrolyte (mode II) are the two main mechanisms for Na penetration, but a comprehensive study of Na penetration in NaSICON is necessary, particularly at high current density. To further understand these modes, this work employs unidirectional galvanostatic testing of Na|NaSICON|Na symmetric cells at 0.1 A cm–2 over 23 h at 110 °C. While galvanostatic testing shows a relatively constant yet increasingly noisy voltage profile, electrochemical impedance spectroscopy (EIS) reveals a significant decrease in cell impedance correlated with significant sodium penetration, as observed in scanning electron microscopy (SEM). Further SEM analysis of sodium accumulation within NaSICON suggests that mode II failure may be far more prevalent than previously considered. Further, these findings suggest that total (dis)charge density (mAh cm–2), as opposed to current density (mA cm–2), may be a more critical parameter when examining solid electrolyte failure, highlighting the challenge of achieving long discharge times in batteries using solid electrolytes. Together, these results provide a better understanding of the limitations of NaSICON solid electrolytes under high current and emphasize the need for improved electrode–electrolyte interfaces.