This is most likely caused by using a cheapo no-name commodity router. These devices usually sell for 30-200$ in retail stores, and are made with the cheapest components their manufacturers can find, and the bare minimum of memory is installed in order to maximize profit per unit. While the speed of the traffic is not usually an issue for these devices, they are not designed to have large amounts of tcp/ip connections managed in their state tables, which is inherently caused by the bit torrent protocol.
If you are doing serious downloading I recommend using a dedicated older pc and pfSense as a router/firewall, which will guarantee rock solid connections, as well as it comes with a variety of other benefits such as bandwidth monitoring, proxy/caching, really easy yet powerful firewall, and more.
If this is not possible, try using a custom firmware on your router, or purchase a router that supports tomatoe or dd-wrt.
Last but not least, you can pick up a Cisco 830 series router for relatively cheap on craigslist or ebay. While moderately difficult to configure, these are also VERY solid devices.