The .REG (if you are referring to that one), is not created when installing. It's only created after a successful activation.
As explained many times on the forum, losing that file is not really a problem: it's NOT required to run GSX, it's ONLY a shortcut that can save you from *manually* typing your Serial Number, but the end result of it, it's that it's simply used to insert your Serial Number in the registry without manually typing it, but you can obtain exactly the same result by using the "Register Serial" function of the Addon Manager, type your Serial Number manually like any other program that use a serial number, and activate it.
After the activation, a new .REG file will be created in your Home folder ( the folder with your name that *contains* your Documents, Pictures, etc.) which, again, can be used the next time to reactivate without having to *type* the serial manually, that's the one and only purpose of that file.