It's definitely possible to run a Zulip server with essentially no downtime. E.g. the main zulipchat.com service has had approximately 10 user-facing outages with a median duration of 5-10 minutes over the last 5 years (there was one while we still only had a few hundred users that lasted overnight), most of them in the middle of the night. Happy to talk more about this for anyone curious; there are some fun stories (like migrating from MySQL to Postgres as our primary database technology with <30 minutes of downtime early in its development).
We don't have a public uptime SLA for zulipchat.com uptime yet, but we're happy to make them for individual customers (and I suppose we should add one).
If you're self-hosting, our commercial support offerings will help you setup your servers in a way that achieves your uptime goals; because Zulip is so stable, usually folks just go with a hot spare (our enterprise customers generally only report downtime related to server upgrades, which is usually avoidable).