If an EC2 elastic agent is associated with an Elastic IP, either through the AWS console or a start-up script, Bamboo loses connection to the agent.

This is probably because Bamboo insist on communicating with the agent using the instance's original public DNS name/IP, rather than the new one assigned by Elastic IP/DNS name.

Elastic (static) IP support would be extremely useful for example if the build process requires connection to a remote server which is behind a firewall. The remote firewall can be configured to allow a single IP through rather than completely exposed.