The Internet of Things (IoT) refers to a broad variety of objects with communication capabilities that are integrated into Internet. The interconnection between those objects and the Internet is enabled thanks to border routers. In this article, we investigate the aftermath of the failure of border routers on ongoing communications. Next, we propose to overcome the exposed problems by providing objects with multiple border routers. The corresponding subnet is therefore multihomed, i.e. all objects in this subnet are reachable via multiple paths, one per active border router. Whenever a border router fails, we dynamically re-route traffic to an active border router. Such flows redirection remains transparent to remote peers. Our solution, referred to as Syn-RPL, is based on the well-known IPv Routing Protocol for Low-Power and Lossy Networks (RPL). Syn-RPL is evaluated through experimentations on a real testbed.