No, the railroad isn't closed. It starts running at park open and runs continuously - at times they can have two or three trains running - so there isn't a set schedule, which is probably why the website says the schedule is unavailable. It usually stops sometime in the evening though, before the fireworks. The actual time it stops that day will be in the Times Guide you can pick up at the entrance to MK.
We love the RR and frequently ride it all the way around and more! Missed it when it was down for rehab last year!