I have a Synology DS416play, just turned four years old, that drops off the network once a week. It started doing this about four months ago. The machine still appears to be running (power light on), but I have to do a forced shutdown and restart to get things back to normal. Not something I like to do to computers. The Synology is plugged via Ethernet directly into a FiOS router.
Obviously, something changed. Perhaps a DSM update or something. I always access the NAS from my Mac Book Pro every day when I am on the same network; which of course is not every day. The NAS is not exposed to the Internet; just local.
I have no clue why this is happening.