Context. The general prediction that more than half of all cataclysmic variables (CVs) have evolved past the period minimum is in strong disagreement with observational surveys, which show that the relative number of these objects is just a few percent. Aims. Here, we investigate whether a large number of post-period minimum CVs could detach because of the appearance of a strong white dwarf magnetic field potentially generated by a rotation- and crystallization-driven dynamo. Methods. We used the MESA code to calculate evolutionary tracks of CVs incorporating the spin evolution and cooling as well as compressional heating of the white dwarf. If the conditions for the dynamo were met, we assumed that the emerging magnetic field of the white dwarf connects to that of the companion star and incorporated the corresponding synchronization torque, which transfers spin angular momentum to the orbit. Results. We find that for CVs with donor masses exceeding ∼0.04 M⊙, magnetic fields are generated mostly if the white dwarfs start to crystallize before the onset of mass transfer. It is possible that a few white dwarf magnetic fields are generated in the period gap. For the remaining CVs, the conditions for the dynamo to work are met beyond the period minimum, when the accretion rate decreased significantly. Synchronization torques cause these systems to detach for several gigayears even if the magnetic field strength of the white dwarf is just one MG. Conclusions. If the rotation- and crystallization-driven dynamo – which is currently the only mechanism that can explain several observational facts related to magnetism in CVs and their progenitors – or a similar temperature-dependent mechanism is responsible for the generation of magnetic field in white dwarfs, most CVs that have evolved beyond the period minimum must detach for several gigayears at some point. This reduces the predicted number of semi-detached period bouncers by up to ∼60 − 80%.