Hydrogels of numerous chemical compositions have achieved high fracture toughness on the basis of one physical principle. As a crack advances in such a hydrogel, a polymer network of strong bonds ruptures at the front of the crack and elicits energy dissipation in the bulk of the hydrogel. The constituent that dissipates energy in the bulk of the hydrogel is called a toughener. A hypothesis has emerged recently that tougheners increase fracture toughness greatly but contribute little to fatigue threshold. Here we ascertain this hypothesis by studying hydrogels of two kinds, identical in all aspects except for tougheners. A Ca-alginate/polyacrylamide hydrogel has ionic bonds, which act as tougheners, resulting in a toughness of 3375 J/m2 and a threshold of 35 J/m2. A Na-alginate/polyacrylamide hydrogel has no ionic bonds, resulting in a toughness of 169 J/m2 and a threshold of 17 J/m2. These results motivate a discussion on the development of fatigue-resistant hydrogels.