I've now seen a case where Bittorrent caused problems with a low-end wireless router: Hawking HWR54G Rev M with latest firmware (Version 1.0 Release 11)
After about 24 hours or so of high Bittorrent activity (Azureus 2.4.0.2 client with default settings), the router starts to become very sluggish on the web interface, and will eventually stop responding to DHCP requests. Restarting the router always corrects the problem, and the problem doesn't occur when Bittorrent isn't running.
FWIW< I haven't seen this problem on better routers (with the latest firmware); e.g., D-Link DI-624, NETGEAR WGR614.