The robustness of an optical encryption system directly determines the anti-jamming capability of the ciphertext in the process of storage and transmission, and is always evaluated in the form of the ability against noise and occlusion attacks. The parallel encryption system for multi-channel images based on a joint transform correlator can encrypt the multi-channel images simultaneously into a single ciphertext, and also recover the arbitrary original images with corresponding keys. The robustness of this system is simulated and analyzed. The results show that the decryption effect of each channel is reduced obviously when the ciphertext area is cut by 50%. The correlation coefficient (CC) values between some original and decryption images get the level of about 0.2. The reason is analyzed and the arrangement of the joint power spectrum is optimized. The simulation results show that not only the robustness of the encryption system is significantly improved, especially when the ciphertext area is cut by 60%, the CC values of all channels are greater than 0.49, but also the advantage on resisting noise attacks can be maintained. Finally, an optical experiment system is built to verify the effectiveness of the proposed method for improving the robustness of the encryption system.