I use Safari and got that message a few days ago. I waited a few minutes, reloaded the page & tried again, and it worked. Have since made bookings without that reoccurring.
Same room each time? It's possible you are trying to book a room that is actually sold out. Sometimes the website can glitch and show a room that isn't available. Or isn't really available for every night. Especially when you were trying to book the last one. It's possible for both you and someone else tried to add the same last room in your cart, then the other person check out and actually book the room but the room doesn't every drop out of your cart. I'd call in your shoes, and I hate calling Disney. But if it has done it on all computers and browsers and done it for days there's something else afoot
