I think this may sound familiar to many... Are you away from home when you suddenly need to access remotely your cameras or any other service hosted in your home, BUT your network/internet at home has stopped responding ? You are exactly in the right project.
To solve that, this device will keep pinging some pre-configured websites (or IP addresses) like google.com, google dns, microsoft, facebook... etc.. and then, when none of them respond to a ping after three tries, a relay cuts off power to the cable modem (or to your router as well) for 10 seconds, then a reboot and new sync with the provider will be done.
This is what you will need to build this:
ARDUINO UNO (or ATMEGA328p Standalone) W5100 ETHERNET MODULE RELAY MODULE
Code is available at www.zolalab.com.br