In the present investigation we revisit the widely-used locally-constant field approximation (LCFA) in
the context of the pair-production phenomenon in strong electromagnetic backgrounds. By means of
nonperturbative numerical calculations, we assess the validity of the LCFA considering several spatially
homogeneous field configurations and a number of space-time-dependent scenarios. By studying the
momentum spectra of particles produced, we identify the criteria for the applicability of the LCFA. It is
demonstrated that the Keldysh parameter itself does not allow one to judge if the LCFA should perform
accurately. In fact, the external field parameters must obey less trivial relations whose form depends on the
field configuration. We reveal several generic properties of these relations which can also be applied to a
broader class of other pair-production scenarios.