Ec2 instance goes unresponsive - instance unreachablity error - status check failed

The instance status check fails when the instance load is high, such as memory depletion, as described in this document.
https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/monitoring-system-instance-status-check.html#types-of-instance-status-checks

So the reason why we can no longer connect to your instance is because of the heavy load.
Possible countermeasures include using a larger instance size than now or selecting an instance type that is appropriate for the application workload.
https://aws.amazon.com/ec2/instance-types/?nc1=h_ls

Also, if you are able to deploy load balancing workloads, consider deploying an ELB in front of the instances to distribute the load among multiple instances.

2/2 checks for system and hardware faults. In either in systems faults stop and reboot the instance. This should replace the faulty EBS image with a new image of an instance. For hardware fault perform a termination of the EC2 and then launch a new EC2 instance.

Use CloudWatch the monitor the CPU and Memory Disk and Network Metrics Data points in the Log stream Group. Stop the instance and change the instance type accordingly.