In this study, the authors present monopulse beam synthesis methods with sparse elements robust to the antenna module failure. The monopulse beam radar generates two beams (sum/difference beams) simultaneously and it requires a large number of antenna elements in antenna arrays. However, it is desirable to reduce the number of active antenna elements. Furthermore, in many practical applications, some of antenna elements may experience the module failure. Accordingly, to design beams robust to the module failure and reduce the number of active antenna elements simultaneously, the authors propose a modified reweighted L1 minimisation methods in which the Bayesian-inference-based failure probability is exploited. The authors also discuss how the proposed sparse beam synthesis method can be carried out successfully in conjunction with the array failure diagnosis based on the Bayesian compressive sensing.