Some of my tablemates on a cruise (not on RCCL) were on back-to-back cruises. In their case, they were notified upfront that they might have to change cabins, but a day or two before the end of the first week, they learned that they got to stay in the same cabin. In that case, they did not have to leave the ship.
To be sure of your situation, ask your travel agent. If you didn't use one, you'll have to contact the cruise line to find out.