What does your app status look like (flyctl status --all)? Perhaps flyctl vm stop ... helps you get unstuck (ref)?
On every flyctl deploy, your app process gets a new VM to run in.
If you’re using Machines (Apps v2), and If you want your app process to move to another host, then try cloning (flyctl m clone ...) the VM, preferably to another region (docs).
If you’re using Apps v1, then decreasing and increasing scale count (flyctl scale count <n>) is one way new VMs may be provisioned (same as flyctl deploy), with (what I’d imagine) higher chances of the app process landing on a different host.