  We report a comprehensive study of the spin ladder compound
BaFe$_2$S$_{2.5}$Se$_{0.5}$ using neutron diffraction, inelastic neutron
scattering, high pressure synchrotron diffraction, and high pressure transport
techniques. We find that BaFe$_2$S$_{2.5}$Se$_{0.5}$ possesses the same $Cmcm$
structure and stripe antiferromagnetic order as does BaFe$_2$S$_3$, but with a
reduced N{\'{e}}el temperature of $T_N=98$ K compared to 120 K for the undoped
system, and a slightly increased ordered moment of 1.40$\mu_B$ per iron. The
low-energy spin excitations in BaFe$_2$S$_{2.5}$Se$_{0.5}$ are likewise similar
to those observed in BaFe$_2$S$_{3}$. However, unlike the reports of
superconductivity in BaFe$_2$S$_3$ below $T_c \sim 14$~K under pressures of
10~GPa or more, we observe no superconductivity in BaFe$_2$S$_{2.5}$Se$_{0.5}$
at any pressure up to 19.7~GPa. In contrast, the resistivity exhibits an upturn
at low temperature under pressure. Furthermore, we show that additional
high-quality samples of BaFe$_2$S$_3$ synthesized for this study likewise fail
to become superconducting under pressure, instead displaying a similar upturn
in resistivity at low temperature. These results demonstrate that microscopic,
sample-specific details play an important role in determining the ultimate
electronic ground state in this spin ladder system. We suggest that the upturn
in resistivity at low temperature in both BaFe$_2$S$_3$ and
BaFe$_2$S$_{2.5}$Se$_{0.5}$ may result from Anderson localization induced by S
vacancies and random Se substitutions, enhanced by the quasi-one-dimensional
ladder structure.
