The inactivity timer is user inactivity, not system inactivity. If it was based on the system, it would never sleep since services wake up to run their jobs, scheduled tasks may run, your anti-virus may make a background scan. You'll notice that Windows itself is hardly ever idle for more than a few seconds (which isn't a problem).
There are multiple ways to get your system to stay awake, the easiest of them is to create a new power profile that either extends (say 4 hours) or completely turns off the sleep timer while you are encoding.
Another, cheap and easy way, is to load a video or audio file in Windows Media Player, and pause it. This will cause WMP to tell the system not to sleep because it is "playing" a media file.
Most encoders I've seen (well, the wrapper programs anyway) allow you to tell it to perform an action when complete or to prevent sleeping while it's running. Unfortunately, there isn't really anything you can do when copying files though, other than the above advice.