Trying to book train on May 23 from Roma Termini to Fiumicino Airport via Trenitalia website and continue to get message - this booking is not available. Is it possible the train is sold out for all times between 6:00 AM and 10:00 AM?
No reservations offered or needed on the Leonardo Express. Buy your ticket at a Tabachi shop in Termini ( € 11) and hop aboard; they run every 30 minutes.
No, the trains are not sold out. The Leonardo Express is a regional train and for regional trains the Trenitalia site only shows fares and allows booking just a few days in advance. But there is no need to book now. Buy your ticket in Rome or at any station in Italy.
The Leonardo Express runs every 30 minutes. As Tim says, its a local Regionale train. No reservations permitted. You can easily buy a ticket when you first arrive in Rome. But, you'll get a surprise there. The ticket for a Regionale train is an open ticket good for 60 days. No specific train, date of travel or seat reservation. You can tell the ticket agent which train you want and he'll still sell you the same ticket. This means that you can hop on any Leonardo Express that you want. It's like your local bus system. You show up, get on and find a seat. If no seat, you stand. Best Hint: show up early for the train run you want, validate your ticket and walk down the platform a bit to where the carriages stop and be early in line to get on. First there, first on. That's the Regionale.