Methods and apparatus for handling failure of traffic forwarding (TF) systems in networks that include multiple zones each including a TF system between a production network and a border network. A TF system advertises routes in its zone and handles egress of packets from sources on the local production network onto the border network. TF systems may also advertise low-priority routes in other zones. If a TF system in a zone fails, sources in the zone may make connection requests to the low-priority routes. Instead of egressing the packets onto the border network, the requests on the low-priority routes are responded to with reset messages. Thus, the sources do not have to wait for a connection timeout, and packets for destinations in the zone are not egressed onto local border networks in other zones and sent through thin pipes between the local border networks.