Motivated by indirect observational evidence for strongly magnetized accretion discs around black holes, and the novel theoretical properties of such solutions, we investigate how a strong magnetization state can develop and persist. To this end, we perform local simulations of accretion discs with an initially purely toroidal magnetic field of equipartition strength. We demonstrate that discs with zero net vertical magnetic flux and realistic boundary conditions cannot sustain a strong toroidal field. However, a magnetic pressure-dominated disc can form from an initial configuration with a sufficient amount of net vertical flux and realistic boundary conditions. Our results suggest that poloidal flux is a necessary prerequisite for the sustainability of strongly magnetized accretion discs.