Persistent or local Greengrass group deployment in Docker container

When I deploy a Greengrass group on a GGC running in a Docker container, as far as I can tell the group exists as long as the GGC image is running, and if the GGC image is restarted the group is not present and requires redeployment. I have thus far been redeploying from the AWS IoT console, but my use scenario has the core device powered on and off with relative frequency, with no guarantee of Internet connection.

I would like to find a way to have the group details and associated functions persistent between sessions, or be saved and redeployed locally.