Requested twice, moved twice. The first time (2013), we booked in December for a May cruise, and moved sometime around January. This last time (2019), we booked in in August for the first week of April, but didn't get moved until abou two weeks before the trip.
Some here will tell you to be the squeaky wheel to get moved. I don't think that has anything to do with it. I did periodically check to confirm I was still on the list, and one time was politely told "you are on the waitlist, just let the process work like it usually does, and ask to be moved when you board if it doesn't." My guess is there is a priority of some sort based on when you make the request, the status you have with the cruise line, the party size, etc. I am sure they just work through the list based on the order you are assigned. I also suspect they have a very limited number of main dining spots available at the time of booking, so they have flexibility for concierge and other needs. Then they slowly start filling main dining as the cruise gets closer, with final assignments about two weeks out (when we got moved last time).