An efficiency-enhanced procedure to treat continuous-time, high-cycle fatigue (HCF) constraints in topology optimization is presented. The HCF model predicts the evolution of fatigue damage at each point in the design domain using a system of ordinary differential equations. We employ gradient-based optimization and the fatigue sensitivities are determined using adjoint sensitivity analysis. As the predicted damage has history dependence, adjoint variables are solved via a stepwise backward procedure. Therefore, the computational cost increases in proportion to the number of time steps. To reduce this cost, we propose an extrapolation technique which is valid for all forms of periodic, proportional loads and most non-proportional loads and allows treatment of essentially an unlimited number of load cycles. Using this technique, several problems in both 2D and 3D are solved numerically where the objective is to minimize structural mass subjected to a fatigue constraint.