It's possible this is a permissions problem. Have you checked the permissions of the folder?
You check system and exception log? Any errors?
You installed security patches SUPEE 6788 before 7405. You can read more here: https://community.magento.com/t5/Security-Patches/magento-1-9-1-1-SUPEE-7405-saving-rejects/m-p/2739...
This happens with any patch that fails, it says it saved rejects, but it never does. I just want to know when it fails why I have no .rej file to review. Does anyone know what might cause .rej file creation failure.