The only recovery was a reboot — which just restarted the 49.7-day countdown.

Saying 'time bomb' made me think this was unfixable after the expiration happened.

Pings still worked. Existing connections stayed alive. But anything that needed a new TCP socket simply failed.

Sounds like system admin hell for servers running on a string.

Huh, I use a MacBook headless in clamshell mode and have it stop responding over the network every so often. I wonder if this is why.