  Informative recent measurements on the heavy-fermion metal $\rm
\beta-YbAlB_4$ performed with applied magnetic field and pressure as control
parameters are analyzed with the goal of establishing a sound theoretical
explanation for the inferred scaling laws and non-Fermi-liquid (NFL) behavior,
which demonstrate some unexpected features. Most notably, the robustness of the
NFL behavior of the thermodynamic properties and of the anomalous $T^{3/2}$
temperature dependence of the electrical resistivity under applied pressure $P$
in zero magnetic field $B$ is at variance with the fragility of the NFL phase
under application of a field. We show that a consistent topological basis for
this combination of observations, as well as the empirical scaling laws, may be
found within fermion-condensation theory in the emergence and destruction of a
flat band, and explain that the paramagnetic NFL phase takes place without
magnetic criticality, thus not from quantum critical fluctuations. Schematic
$T-B$ and $T-P$ phase diagrams are presented to illuminate this scenario.
