  In Ti-intercalated self-doped $1T$-TiSe$_2$ crystals, the charge density wave
(CDW) superstructure induces two nonequivalent sites for Ti dopants. Recently,
it has been shown that increasing Ti doping dramatically influences the CDW by
breaking it into phase-shifted domains. Here, we report scanning tunneling
microscopy and spectroscopy experiments that reveal a dopant-site dependence of
the CDW gap. Supported by density functional theory, we demonstrate that the
loss of the longrange phase coherence introduces an imbalance in the
intercalated-Ti site distribution and restrains the CDW gap closure. This local
resilient behavior of the $1T$-TiSe$_2$ CDW reveals a novel mechanism between
CDW and defects in mutual influence.
