An AMI image is an image of an EC2 instance at a given point in time, like a photograph. When you launch an EC2 instance from an AMI, the AMI is not considered running. The AMI is copied to your EC2 instance and your EC2 instance is running. The original AMI image is not affected (and cannot be affected) by any changes done to your EC2 instance.
If you make changes to your EC2 instance and you want to preserve them in an AMI, you must create a new AMI image. When you do this, you can delete the old AMI image if you don't need it anymore, or keep it around if you are going to want to launch new EC2 instances from before you made your configuration changes.