That depends. At a high level, in order for your HSI service to say "up," if you've lost electricity at you house your cable modem and any essential network devices would have to have their own backup power (e.g. UPS) so that they could continue to operate during the power outage.
The various network devices between the head-end and your cable modem have backup power available to keep them running during comercial power failure. Most distribution systems are actively monitored and will continue to operate on batteries for a number of hours. In this scenario, as battery capacity starts to dwindle below a certain standard, a technician is dispatched to the power suply and a portable generator is connected -- thus, keeping the connection alive. Other systems have backup generators which can maintain operation of the system as long as there is a fuel source.