statuscheckfailed_instance still unreachable after reboot and shutdown restart

Based on the information provided, it appears that your EC2 instance is experiencing a reachability issue after running AWS-RunPatchBaseline and rebooting. This situation can occur due to various reasons, and there are several steps you can take to troubleshoot and potentially resolve the issue:

1. Check instance status checks: Ensure that both system and instance status checks are passing. If they're failing, this could indicate underlying hardware or software issues.

2. Review console output: Examine the instance console output for any error messages or unusual behavior during the boot process. This can provide valuable insights into what might be preventing the instance from becoming fully operational.

3. Analyze CloudWatch metrics: Check the CPU utilization and other performance metrics in Amazon CloudWatch. High CPU usage or memory exhaustion could cause the instance to become unresponsive.

4. Verify network configuration: Ensure that the security groups and network ACLs associated with the instance are correctly configured and not blocking necessary traffic.

5. Check EBS volumes: Verify that all attached EBS volumes are properly mounted and accessible to the instance.

6. Investigate SSM Agent: The error message indicates that the SSM Agent is not online and unable to connect to the Systems Manager endpoint. This could be due to network connectivity issues or problems with the SSM Agent itself.

7. Consider OS-level issues: Since you can see the login screen in the console screenshot, the operating system seems to be booting. The problem might be related to network services or SSH configuration.

If these steps don't resolve the issue, you may need to consider more advanced recovery options:

1. Create a snapshot of the instance's root volume.
2. Attach the root volume to another instance as a secondary volume to investigate further or recover data.
3. If necessary, launch a new instance from a recent backup AMI and restore your data.

If you're unable to resolve the issue through these methods, you may need to contact AWS support for further assistance, especially if you suspect there might be an underlying hardware problem with the EC2 host.

Remember to always maintain regular backups and consider using an Elastic IP address to make it easier to remap your public IP if you need to stop and start your instance during troubleshooting.

Sources
Troubleshoot status check failures on an unreachable EC2 Linux instance | AWS re:Post
Instance keeps on failing with status check - reachability issue | AWS re:Post
Troubleshoot an unreachable Amazon EC2 instance - Amazon Elastic Compute Cloud