Running a restaurant kitchen, what equipment maintenance should be on a schedule so things do not break mid-service?

You are right that in a commercial kitchen nearly every breakdown traces back to a skipped routine, and in this heat the margins are tighter, so a schedule genuinely pays for itself in avoided downtime and spoiled stock. The core items to put on a calendar: refrigeration first, because it is the top failure point here, clean the condenser coils and check door seals and temperatures regularly (monthly is sensible), as clogged coils in the heat are what kill compressors; the extraction hood and its filters need a regular deep clean for both suction and fire safety; gas equipment wants periodic safety and burner checks; and the dishwasher needs descaling and cleaning because the hard water scales it up fast and wrecks the elements. Beyond that, ice machines, combi ovens and any water-fed equipment all benefit from scheduled descaling. The trick is to write it as a simple calendar (monthly, quarterly, annual) and actually log each service, so nothing quietly lapses until it fails at peak time. Putting the recurring work with a team that does kitchen equipment maintenance on a set schedule is far cheaper than emergency callouts mid-service. Refrigeration and the dishwasher are where I would start — commercial-kitchen makers such as Electrolux Professional publish recommended service intervals for exactly this equipment. They fail most and cost most when they do.