The polymerized network of the cytoskeleton of the red-blood cell (RBC) contains different protein components that maintain its overall integrity and attachment to the lipid bilayer. One of these key components is the band 3-ankyrin complex that attaches the spectrin filaments to the fluid bilayer. Defects in this particular component result in the shape transformation called spherocytosis, through the shedding of membrane nano-vesicles. We show here that this transition and membrane shedding can be explained through the increased stiffness of the network when the band 3-ankyrin complexes are removed. ATP-induced transient dissociations lead to network softening, which offsets the stiffening to some extent, and causes increased fragility of these mutant cells, as is observed.