Looks like the device gets disconnected and reattached when you trigger that reset, causing the permissions to change.
Assuming you’re not mixing multiple of those USB serial devices, it may be easiest to manually mknod a copy of ttyUSB0, chown it to the right uid and gid and then bind-mount that into the container.
An alternative would be to setup a udev hook on your host which would fix the permissions whenever the device re-appears.