I also use Firefox, and broadband and don't have your problem. When you click "download", is that when it slows down? I find most files (except some of the really big ones) download in anything from seconds to under a minute. So, they are far too quick for the system to time out.
I just downloaded a 21mb comic in 12 seconds so it might be your internet connection. All I did was click download and Firefox asked me where I wanted the file to go: I pointed it to my "downloads" file, clicked "o.k." and the download started, and there it was. Perhaps narfstar and Mark can shed more light on your problem.