  We study the beam-normal single-spin asymmetry (BNSSA) in high-energy elastic
electron scattering from several spin-0 nuclei. Existing theoretical approaches
work in the plane-wave formalism and predict the BNSSA to scale as $\sim A/Z$
with the atomic number $Z$ and nuclear mass number $A$. While this prediction
holds for light and intermediate nuclei, a striking disagreement in both the
sign and the magnitude of BNSSA was observed by the PREX collaboration for
$^{208}$Pb, coined the "PREX puzzle". To shed light on this disagreement, we go
beyond the plane-wave approach which neglects Coulomb distortions known to be
significant for heavy nuclei. We explicitly investigate the dependence of BNSSA
on $A$ and $Z$ by i) including inelastic intermediate states' contributions
into the Coulomb problem in the form of an optical potential, ii) by accounting
for the experimental information on the $A$-dependence of the Compton slope
parameter, and iii) giving a thorough account of the uncertainties of the
calculation. Despite of these improvements, the PREX puzzle remains
unexplained. We discuss further strategies to resolve this riddle.
