The uTorrent transport protocol (uTP) was designed to make bitTorrent more ISP friendly by controlling the P2P traffic bandwidth. However, it may cause your router/modem to lose internet connectivity for your device, especially earlier models of the router.
I have seen quite a few people complaining about lost of connectivity after bitTorrent starts (especially after upgrading to latest versions of the clients) either immediately or after a while. People have been blaming it on firewalls, anti-virus or even NAT overflow, but to no avail. The solution may be very simple – just turn off uTP Bandwidth Management in your bitTorrent client.