  We study the competition between Kondo screening and frustrated magnetism on
the non-symmorphic Shastry-Sutherland Kondo lattice at a filling of two
conduction electrons per unit cell. A previous analysis of this model
identified a set of gapless partially Kondo screened phases intermediate
between the Kondo-destroyed paramagnet and the heavy Fermi liquid. Based on
crystal symmetries, we argue that (i)~both the paramagnet and the heavy Fermi
liquid are {\it semimetals} protected by a glide symmetry; and (ii)~partial
Kondo screening breaks the symmetry, removing this protection and allowing the
partially-Kondo-screened phase to be deformed into a Kondo insulator via a
Lifshitz transition. We confirm these results using large-$N$ mean field theory
and then use non-perturbative arguments to derive a generalized Luttinger sum
rule constraining the phase structure of 2D non-symmorphic Kondo lattices
beyond the mean-field limit.
