The process nobody was supervising
It was started by hand, it survived for months, and then the machine rebooted.
A small application ran on a port behind the web server. Somebody started it over SSH one afternoon, it worked, and everybody moved on.
The machine rebooted for a kernel update at two in the morning. Nothing brought the application back. It stayed down four and a half days, and the first report came from a customer, because nothing on our side was watching the port.
A process that is running is not a process that is supervised. Put it under something that restarts it when it dies and starts it when the machine boots, and then prove it by restarting the machine, not by looking at the process list.