We have only received a complimentary upgrade one time - on our last trip.
I think it resolves down to a few simple decision points:
* Are there plenty of rooms available? Obviously if you are there during a busy time it will be hard to get an upgrade because the resort needs to keep the 'better' rooms ready for the customers that have reserved them.
* Will giving the upgrade cost the resort any money? I think it is especially rare for someone to be upgraded to a concierge room because the resort actually has some expense associated with the upgrade - as opposed to an upgrade from a Garden View to a Lagoon View which doesn't really cost them anything.
* And finally - Is there a REASON...? If you show up trailing tin-cans and a big sign that says 'Just Married' you have a better shot at an upgrade
Our stay at AKL last Nov/Dec met all three of the above. AKL (all of WDW really) was very empty when we visited so there were plenty of rooms available, the upgrade didn't cost the resort any money (standard to standard-savannah), and when we checked in I actually made an effort to give the check-in lady a reason. I mentioned that we typically stayed at the Poly (a slight exaggeration, although we have stayed there more than any other resort), that we had just come from the HRH - and it had really impressed us, and that we were giving the AKL a try because we had to be careful with money on this trip.
It worked - when she handed me the map/keys she pointed out that we would be in a Savannah view and hoped that we would "have an extra magical visit" with them (if memory serves).
As I say - it's never happened before so it may merely have been pure luck.