The discontinuous uptake and release of surfactants by hydrogels and the accompanying discontinuous volume transition is known to occur with a hysteresis. We have performed a theoretical analysis in order to find the mechanistic origin of this phenomenon. Using a mean-field model, we have quantitatively reproduced the experimental behavior by considering the cost of elastically deforming the gel material to allow phase coexistence. The major part of the hysteresis is due to the high phase coexistence cost of the swelling transition, since in this direction the coexistence cost depends not only on the elasticity of the network (being a weak force in comparison) but also on the entropy of the monovalent nonsurfactant electrolyte present in the system.