This is on Windows Client 10.2, so it's possible it changed on a later version...

There are these files:
C:\Program Files (x86)\Laserfiche\Client\en\Search.htm
C:\Program Files (x86)\Laserfiche\Client\en\SearchTypes.js

These files dictate the behavior and appearance of the search functionality.  I've been able to make small tweaks to the HTML (like to font size or color) and have it reflected, so I know the system is using those files to generate the search fields.

I recommend saving a copy of these two files under different names (in case you need to revert back to them), and then replacing them with copies from another workstation that doesn't have the issue (make sure it's the same version).

If that doesn't work, it may require a repair or reinstall or .NET or something similar.  If you actually inspect those two files I mentioned above, you can see there is some vbscript code that enables that second field when the appropriate checkboxes are marked, so it's possible that something else is corrupted that could be causing the vbscript to fail.  However, if that is the case, you'd probably be seeing a lot of other behavior in those search options failing as well (like the different checkboxes on the "Field Search" options) and if you are not seeing that, I don't think it would be a global issue running the script.