A method is disclosed that enables mitigating at least some of the problems caused by a packet attack. When a first Internet Protocol (IP)-capable device is subjected to a packet attack, it indicates periodically to a second IP-capable device that certain communications with the first device are to be suspended. The periodic transmitting of the indication is performed at a slower rate than the keep-alive mechanism that is normally used to detect loss of connectivity. When the second device receives the transmitted indication, it refrains from transmitting keep-alive messages to the first device for a predetermined interval. Meanwhile, the first device also refrains from transmitting keep-alive messages to the second device for a similar interval. In transmitting the suspend indication, the illustrative embodiment seeks to prevent pairs of communicating devices that are experiencing packet attacks from continuing their operation under the erroneous assumption that each device is unavailable.