Ec2 instance static private ip address

You tagged this amazon-vpc, but the behavior you describe is what happens when an instance is launched in EC2-Classic. When you launch an instance in a VPC, it is assigned a private IP address and it remains for the lifetime of the instance. Their documentation is pretty clear on that point. To be clear, 'instance' in this case is a discrete 'i-' number.

EC2-Classic has no support for what you're looking for, and you can't assign new interfaces to it.

If you're not actually keeping the same instance defined and are spinning a new one up in a VPC based off of an AMI you have, you will get a new private IP address each time. As you suspected, if you define a new Interface and associate it with the instance, that Interface will have a static IP address. When you terminate the instance, the extra Interface goes unassigned. Reassign it to a new instance when you spin one up.