My Production EC2 Instance randomly became unresponsive and is now stuck in stopping state.

You can check this article about troubleshooting an EC2 instance

As this is production, the best path is to open a technical support case.

To have more visibility about what is happening you can enable cloud watch log for the EC2 instance, so you have a log outside the instance that can help you diagnose, also monitoring metrics on Cloudwatch can help know if this a resource related issue. These articles might help:

• Cloudwatch logs on EC2
• CloudWatchUnifiedAgent