Not really, it is upto the entrypoint process to keep around a Machine alive for as long as it wants to (including leaving it up forever). For ex, the Machines I run are set to go down after 180s of inactivity. From the logs, I see that a couple Machines have been up for 12 hours now, presumably since there might have been no inactivity long enough to trigger a self-exit.
In fact, if anything, Fly struggles with short-lived (think 60s or less) Machines: Machine did not have a restart policy, defaulting to restart - #12 by kurt
As for ws, with fly-replay: app=<name>; instance=<id> http-header, you’d be able to pin clients to a specific machine.