When does a turbine need to go to maintenance?
This is a very broad question, but if we limit ourselves to just high bypass turbofans, such as the CFM56 or LEAP-1A used on the A320, and limit "maintenance" to mean major maintenance that requires the engine to be removed from the wing, then the primary driver is typically the total number of flights.  Depending on the engine, it would be removed from the wing for a complete teardown, inspection, and rebuild perhaps every 5,000 - 10,000 flights (typical lifetime of the engine could be between 30,000 and 50,000 flights). Many major components are limited by low cycle fatigue (LCF) driven by thermal stress, so the cold-hot-cold cycle of a flight is what drives the maintence interval, more so than the total flight hours.  i.e. a 1 hour flight and a 12 hour flight are pretty similar in how much they wear out the components.