The public IP address of a running EC2 instance, as it is, is reallocate each time you stop or restart the instance. In order to have a persistent public IP address you have to use Elastic IPs.

1. Open the AWS EC2 Management Console
2. Under Network & Security, click Elastic IPs
3. Click Allocate New Address: this will allocate a static IP address
   
4. Go back to the Elastic IPs table, select the new address, and under the menu Actions choose Associate address
   
5. Select the desired EC2 instance from the drop down, as well as the private IP address, and click Associate
   
6. Now the new static IP address is associate with your EC2 instance, and it will not change upon stopping or restarting of your instance