Power outage alarm / dead man alarm

I need to build 'something' that will alert me if power goes out at one of remote buildings. I figure that this is going to require an agent (ESP8266 probably) that sends a message or ping on a set interval, lets say 1 minute, to a cloud service like IFTTT. If the cloud service fails to receive a set number in a consecutive pattern, it sends an email or notification through Telegram or Pushover etc.

I figured that webhooks might be the way to go but I need a 'reverse' trigger where the trigger fires when the webhook DOES NOT get received rather than when it does.

I thought about having a system where the agent is powered from backup power but if power goes out, so does the network which prevents the notification. I'm OK with false positives where network goes out (triggering a notification) but power stays on.

Any ideas or suggestions are welcome. I looked at the other examples but they seem to be based on local alarms or SMS, neither of which are a workable solution for me.

I use a system that goes the other way. I have a Pi in my basement checking for water leaks. After a power outage it loses WiFi connectivity. I have another Pi that pings the basement one regularly and if it doesn't get a response after a few tries, it sends me a text message and an email.

That's the kind of thing I need but that second Pi you have needs to be a cloud service for me. Essentially, I think the solution will have the cloud service for the hub, pinging an agent and as long as the agent responds, no action occurs. When the agent doesn't respond after X tries, the cloud service sends a notification.