What's corrupting my ROM?
Strange issue, due the fact you have a custom kernel it might be a better plan (hope you don't have any important things on your phone) to completely wipe your phone and reset to stock. So from CWM just wipe system, (Dalvik) cache, install fresh .ZIP from the internal SD (suppose you can mount the USB in CWM) and (re)install a clean ROM, install GApps and modem [optional], fix permissions, boot phone, good to go. If you can't grab a proper logcat/last_kmsg it's difficult solving this issue to be honest. If it's solved just be sure to make a Nandroid backup and then flash a custom kernel, if something goes wrong you can just reset it back to the current (working) state.