StevenK,
It really depends on how you want to handle it. Personally, I'd probably rewrite the INI file at the end of the INI process and refresh any internal copies of the settings (e.g. re-read the file).
The nice thing about keeping a backup copy is that you can provide a Revert Settings command up to the point they actually exit the program. It's a nice touch I appreciate in graphics packages, but it's not commonly used in other things.
Depending on your users, that may or may not be an advantage. If you can, it might help to ask a few whether or not they'd find such a thing useful. They'll probably say "no," but I think that sort of nicety is like embedding an "in-joke" into a manuscript example. 99 out of 100 readers may miss it, but that 100th one makes it worth while.
Hope this helps...
-- Lance