This study presents a framework for estimating the longitudinal compression–compression fatigue life of unidirectional carbon-fiber-reinforced polymer (UD-CFRP) by linking entropy-based matrix degradation to a fiber micro-buckling criterion. A reference effective fiber-direction shear modulus of 2000 MPa was selected using published shear responses of carbon/epoxy composites. Its degradation was prescribed phenomenologically using $G_{\mathrm{eff}}\left(S_{\mathrm{v}}\right)=G_{\mathrm{ref}}\left(1-D_{\mathrm{v}}\right)$, motivated by the viscous-damage stiffness-reduction factor in the nonlinear viscoelastic matrix model. The resulting entropy-dependent modulus was introduced into the micro-buckling equation to obtain residual compressive strength. The corresponding applied compressive stresses were determined from periodic unit-cell compression analyses; no periodic unit-cell shear analyses were used to identify the modulus. Viscous-entropy accumulation was estimated from single-element tension–compression simulations and extrapolated using a stated phenomenological high-cycle law. Fatigue life was defined by the intersection of applied compressive stress and residual compressive strength. The predicted S–N relationship was compared qualitatively with published longitudinal flexural-fatigue data at 25 °C and 2 Hz. Because the loading modes differ and the reference shear modulus comes from related, rather than identical, material systems, the comparison does not constitute direct experimental validation of compression–compression fatigue life.