The effect of quasi-hydrostatic pressure upon the ferromagnetic ground state of magnetodielectric, double-perovskite La2MnNiO6 is investigated using x-ray absorption spectroscopy and diffraction measurements in a diamond anvil cell. The Mn-O-Ni superexchange interaction that gives rise to ferromagnetism in this cation-ordered structure is stable to at least 38 GPa (380 000 atm). Such unusual stability of a ferromagnetic state to applied pressure can be rationalized in terms of the electronic and crystal structure and should help preserve the outstanding electronic and magnetic properties of this material when grown epitaxially under moderate compressive and tensile strain conditions.