They still have tons of ground-based infrastructure that has all the regular failure modes. I suspect the satellites also route IP traffic statically, and they only do so to a fixed set of ground gateways all operated by Starlink (compared to e.g. Iridium, which makes in-space switching decisions and can at least continue ongoing phone calls between two devices without actually needing a reachable ground gateway).

National telcos manage to take themselves out countrywide from time to time too, so I'd assume the same usual suspects apply: Routing problems, botched global configuration changes etc.

If anything, due to centralization, ubiquitous and effectively free connectivity, and centralization/automation of configuration changes, the blast radius of any given error or malicious action has probably been steadily increasing over the years.