The collapse under pressure of the antiferromagnetic ground state of the potassium-rubidium electro-sodalite is studied using the linearized augmented plane wave with local orbitals method. Special considerations needed for setting up this basis for systems such as the electro-sodalites are discussed. It is demonstrated that the magnetism collapses at a unit-cell volume similar to potassium electro-sodalite and rubidium electro-sodalite. A critical pressure of 8 GPa is predicted. The mechanism behind the collapse is a mixing of the F-center states with the highly diffuse unoccupied p states of the alkali atoms.