This isn't twitter specific, but from what I have seen, things can fail for the following reasons.

Something that autoupgrades would become out of spec, refuse to start due to a change in config files.

A counter would roll over somewhere.

A disk fills up.

A cert expires. A domain name entry expires.

Could be days/weeks/months.

My guess is not very long. I've been on a project with three people where if we all quit, it would run until AWS EKS switched off the version of Kubernetes we were using; I'd expect from experience at FB that there's way more done to keep plates spinning on the Twitter fleet and within a couple of days there would be a SEV that no-one was around to respond to.

Of course they'd actually be pulled down by law enforcement much quicker than that if all their content mods left.