  Non-Hermitian topological systems simultaneously posses two antagonistic
features: ultra sensitivity due to exceptional points and robustness of
topological zero energy modes, and it is unclear which one prevails under
different perturbations. We study that question by applying the pseudospectra
theory on the prototypical non-Hermitian SSH (NHSSH) lattice. Topological modes
are robust with respect to chiral perturbations and sensitive to parity-time
(PT) symmetry preserving perturbations. In fact, the chiral symmetry exactly at
the exceptional point leads to the suppression of its sensitivity,
corresponding to a lower order exceptional point. However, counterintuitively,
they are most sensitive with respect to unstructured perturbations, leaving the
fingerprint of the pertinent higher order exceptional (HEP) point.
