Why aren't you downloading directly? Through someone else's proxy?
Firefox could care less if the monitor is on or off. I have shut off my display when downloading a large linux distro before bed for example and when I wake up 7 hrs later its download has completed.
The only way I can see the download pausing is of this is one of those computers that is an all in one computer is part of the display and the system has a hibernation when power button to display is pressed so it goes to sleep and then when turned on it comes out of this hibernation.