Something installed is messing with the $user object. It's passed by reference throughout CB. If something unsets it then it's going to break CB. Disable non-core CB/Joomla plugins/extensions 1 by 1 until it goes away.
I can not stress the below process enough to avoid these problems.
1. Enable debug mode
2. Set error reporting to maximum
3. Install extension
4. Test
5. Enable extension
6. Test
7. Configure extension
8. Test
This should always be the process. You always need to be aware of the before, during, and after. Having debug mode and error reporting configured ensures errors, notices, warnings, etc.. are always exposed. The only notices you should ignore are strict standards. Nothing else should ever be ignored and should be fixed as soon as possible.
Skipping the above process and installing, configuring, installing, configuring, rinse repeat will guarantee cause issues and you'll have no idea what installed is doing it without constant debugging.