After a battle, sometimes ships get a little green uparrow next to them as shown in the first screen snapshot below. I believe that this means that the ship has acquired enough experience for an upgrade. However, not all ships can actually get an upgrade. When I close the screen shown in the first screen snapshot and select the fleet that had engaged in the battle, only one of the ships can be upgraded as shown in the second screen snapshot below.
What determines whether or not a ship can be upgraded after it attains the target experience level?