Aiming at the high-precision reconstruction of structural function functions caused by the strong nonlinearity of cable load-bearing bridge structures, this study presented a structural system reliability analysis method based on a deep belief network (DBN). A long-span suspension bridge was used as the engineering background to identify the dominant fault path of the structural system and analyze the law of structural fault path transfer caused by the deterioration of the suspender strength. Numerical analysis results show that DBN can capture the nonlinear mechanical behavior of the finite element model of the suspension bridge, thereby making the implicit statically indeterminate functional function explicit and realizing the rapid calculation of component reliability indices. According to the search results of the fault path of a certain suspension bridge, the fault order is suspender, stiffening beam, and main cable. The reliability index of the structural system calculated from the three-layer fault tree is 9.63. The coupling effect of corrosion fatigue damage of the suspender causes the reliability index of the suspension bridge structural system to decrease rapidly. The replacement cycle in the case of the target reliability index is 26 years. The analysis results can provide a theoretical basis for the formulation of suspender replacement cycles and strategies.