In this letter, a robust autonomous timekeeping scheme for navigation constellations based on inter-satellite links is proposed. In this scheme, the clocks in the constellation are divided into two groups to generate two Ensemble Times (ET) respectively, then taking the two ETs as references to evaluate the frequency stability of each clock. Abnormal clocks can be identified and excluded from the clock group. After Fault Detection and Exclusion (FDE), the particle swarm optimization (PSO) algorithm is introduced to calculate the optimal weights of the two clock groups using the ensembled time of the opposite group as references respectively. Based on the optimized weights, the final Inter-satellite Link Time (ISLT) is obtained. The simulation implements ISL measurement precision and clock performance parameters of 8 BDS-3 satellites. Simulation results show that when the stability of the ensembled time is significantly higher than that of the evaluated clock, the evaluation results are very close to the true values. In the case of one abnormal clock, the long-term stability of the ISLT obtained by the proposed scheme reaches $1.6\times10^{-14}$ at $\tau=1\;\text{day}$, which is obviously better than $2.3\times10^{-14}$ at $\tau=1\;\text{day}$ using default weights. After 30 days of autonomous operation, the detrended clock difference is 7.8 ns. The research results provide a reference scheme for the autonomous timekeeping of navigation constellations.