They can send the email letter at anytime a room becomes available. So generally best before final payment for concierge due is when you can receive it. Also maybe a couple of days before sail date. If you want you can try calling every day up until 3 days before sail date. After that try to get to the supervisor's desk to see if any availability.
Like NephieRN mentioned they send it to a bunch of people at same time so you have to quickly call them asap once you get the letter. I missed out a couple of times for a specific room category upgrade because of it too.