Can I get email when instance reachability check failed

You need to wire this up yourself:
Setup an Email-based subscription to an SNS topic.
Setup a CloudWatch Alarm for the metric "StatusCheckFailed"
If the value is 1, your system or instance has failed.
Set the notification to go to that sns topic.

There is a very small charge for the alarm..something like .10/month.

Good luck.

Hello there

You need to create cloduwatch alarm and set SNS topic as alarm action. Please follow below document for detailed step

https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/monitoring-system-instance-status-check.html#creating_status_check_alarms