If they send a signal, and it works, that actually indicates the problem is on your end. For them to send a signal to your modem and tell it to reboot, it HAS to be online and connected to the internet. If your modem isn't online, then it cannot receive the signal to reboot.
Is your device that you are having internet issues with, on WiFi, or ethernet? If it's on WiFi, how far away from the router are you? Are there any solid objects between the your device and the router?
What modem / router are you using? An all in one unit? Is it from Cox, or are they separate units, either way, owned by you?