Reading Amazon's documentation it appears that the default behavior for an EC2 instance to to release the current IP address and reassign a new one at some point in the processes depending on whether you are using Classic or VPC:
EC2-Classic: We release the public and private IPv4 addresses for the instance when you stop the instance, and assign new ones when you restart it.
EC2-VPC: The instance retains its private IPv4 addresses and any IPv6 addresses when stopped and restarted. We release the public IPv4 address and assign a new one when you restart it.
In my environment it would be nice if I could find a way to retain the IP address. Does anyone know of a way to do this with EC2 instances?