In Ti-intercalated self-doped 1T-TiSe2 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 long-range phase coherence introduces an imbalance in the intercalated-Ti site distribution and restrains the CDW gap closure. This local resilient behavior of the 1T-TiSe2 CDW reveals an entangled mechanism between CDW, periodic lattice distortion, and induced nonequivalent defects.