While solid-state batteries (SSBs) comprising poly(ethylene oxide) (PEO) based electrolytes are successfully commercialized already for operation at elevated temperature, the selection of the cathode active material (CAM) has so far been limited to LiFePO$_4$. When using high-voltage CAMs such as LiNi$_{1-x-y}$Co$_x$Mn$_y$O$_2$ (NCM), the cells experience fast capacity fading – the cause of which is not consistently understood in literature. In this study, electrochemical impedance spectroscopy measurements in a three-electrode setup are applied to confirm that the NCM|PEO interface is indeed the Achilles‘ heel in PEO-based SSBs at high voltages. In this regard, the interfacial stability on the cathode side depends not only on the upper cut-off voltage, but also on the molecular weight of PEO, strongly affecting the cell performance. Scanning electron microscopy images of the cathodes after cycling suggest that at high voltages interfacial degradation leads to fragmentation of the polymer backbone and to a decrease in viscosity of the solid polymer electrolyte. Overall, the results help to understand the detrimental processes occurring in PEO-based SSBs in combination with high-voltage cathodes.