It's more likely an issue with the modem than the ISP dropping the connection. Taking the example of torrents, it's a well known occurance that having too many simultaneous connections (in this case, everybody you're trying to download a small stream from) will overload cheap modems (or routers) and break the connection to the ISP (sometimes it'll even crash and require a power cycle to correct, although mine just resets itself around once a week if it gets overloaded). Heat can also cause the same symptom. However normally, modems/routers should have no issue with speed if it's just a direct download (e.g. from RapidShare).
If it is the ISP, it could be that they have a traffic management scheme you're not aware of and, if you're downloading too much/too fast, it that could be the reason they cut you off. However I've never heard of them doing any more than slowing down your internet - cutting off means denial of service which, if it's their fault, gives you the right to complain about poor service.
You could try a new modem, and if that doesn't work, call up your ISP and raise an issue about connectivity and stability. If you are torrenting however, you can set download/upload speed caps within your torrent client. I normally set my upload speed to 25KBs when downloading and unlimited when seeding, but I also set my number of half open connections to 150 (although some sites recommend only 125 if you're on a weaker modem/router). The default was set to 250, and that used to cause my router to reset around twice a day.