  Shift-symmetric Horndeski theories admit an interesting class of
Schwarzschild black hole solutions exhibiting time-dependent scalar hair. By
making use of Lema\^{i}tre coordinates, we analyze perturbations around these
types of black holes, and demonstrate that scalar perturbations around black
hole backgrounds inevitably have gradient instabilities. Taken together with
previously established results, this newly-discovered instability rules out
black holes with time-dependent scalar hair in Horndeski theories.
