Water and oil repellent coatings--so-called superamphiphobic coatings--greatly reduce the interaction between a liquid and a solid. So far, only flat or weakly curved superhydrophobic and superamphiphobic surfaces have been designed. This raises the question of whether highly curved structures or microspheres are feasible. Therefore, we coated microspheres with a superamphiphobic layer and measured the force between the spheres and a liquid. A qualitatively different dependence of the adhesion force on the applied load for superamphiphobic and smooth spheres is detected. Furthermore, we demonstrate both experimentally and theoretically that superamphiphobicity fails below a critical particle radius, depending on topological details and type of liquid. Therefore, this study sets a fundamental physical limit to the application of superamphiphobic layers for small objects with high curvature.