Have you used the "Backup RegKey" method ? Try to run FSX as administrator, just once to backup your key.
Also, keep in mind that the only use for the .REG file is to insert your serial in the registry without having to type it. But, even with no .REG file, as long as you keep your email receipt (and there's a way to retrieve it even if it has been lost), by using the "Register Serial" option, you can activate the product even without a .REG file.