Apparently, Machines don’t wake up on requests to its 6pn address (but they do wake up on requests sent to its Flycast address, if any): Machines app without public ports - #3 by JP_Phillips
Cannot snapshot VMs, just yet: VM Snapshot vs Volume Snapshot - #3 by kurt
You could however attach a volume to the Machine, if data is what you want persisted across reboots. Though, I am unsure if volumes even play nicely with Machines: Fly Machines questions - #8 by jgoux | Machine fails if a volume is attached
Your best bet is to fly m clone from an existing Machine’s docker image, if that suits your use-case.