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I use uptime robot http://uptimerobot.com for monitoring, they have a free plan or paid if you want faster checks.

If it's truly critical to have no down time then you probably need to build that resilience in to your architecture.

+1 for UptimeRobot. Learned about it right here on HN:

You need monitoring. But it will not keep your servers from dying.

Using serverless, PaaS like Heroku or similar will help.