Restore Beanstalk Resilient Environment Without Losing ElasticIP

Question

I created an elastic beanstalk environment with VPC. Sometimes the environment is blocked by deploying a version of the code and needs to be rebuilt. When this happens, I lose my Elastic IP.

I tried disabling EIP before rebuilding, but it is still replaced. What can I do to make EIP permanent !? (Yes, I need EIP, and CNAME is not enough for my purposes)