  Period bouncers are cataclysmic variables (CVs) that have evolved past their
orbital period minimum. The strong disagreement between theory and observations
of the relative fraction of period bouncers is a severe shortcoming in the
understanding of CV evolution. We test the implications of the hypothesis that
magnetic braking (MB), which is suggested to be an additional angular momentum
loss (AML) mechanism for CVs below the period gap ($P_\mathrm{orb}\lesssim 120$
min), weakens around their period minimum. We compute the evolution of CV
donors below the period gap using the MESA code, assuming that the evolution of
the system is driven by AML by gravitational wave radiation (GWR) and MB. We
parametrize the MB strength as $\mathrm{AML_{MB}}=\kappa\mathrm{AML_{GWR}}$. We
compute two qualitatively different sets of models, one where $\kappa$ is a
constant and the other where $\kappa$ depends on stellar parameters. We find
that two crucial effects drive the latter set of models. (1) A decrease in
$\kappa$ as CVs approach the period minimum stalls their evolution so that they
spend a long time in the observed period minimum spike ($80\lesssim
P_\mathrm{orb}/\,\mathrm{min}\lesssim 86$). Here, they become difficult to
distinguish from pre-bounce systems in the spike. (2) A strong decrease in the
mass-transfer rate makes them virtually undetectable as they evolve further.
So, the CV stalls around the period minimum and then `disappears'. This reduces
the number of detectable bouncers. Physical processes, such as dynamo action,
white dwarf magnetism, and dead zones, may cause such a weakening of MB at
short orbital periods. The weakening magnetic braking formalism provides a
possible solution to the problem of the lack of period bouncers in CV
observational surveys.
