The pyramid that CANNOT be inverted in a stable ecosystem, is the...

The pyramid of energy is always upright and can never be inverted in any ecosystem. This is because when energy flows from one trophic level to the next, a significant amount of energy is always lost as heat to the environment at each step, in accordance with the second law of thermodynamics. Only about $10\%$ of the energy is transferred to the next trophic level.

The pyramid of number can be inverted in a tree ecosystem where a single tree supports numerous insects.

The pyramid of biomass can be inverted in an aquatic ecosystem where a small standing crop of phytoplankton supports a larger standing crop of zooplankton.

Answer: Energy