DCUO Character stuck in Battle Mode?

In-Combat is indicated by the circle with your stance on your player frame (health bar) blinking. You will be in-combat until an encounter is over, resets, or you rally (and don't get hit/use an ability when you get up). Area 51, you start in-combat from the spawn point, usually by being scanned by a floating drone. Try leaving the orange area on your minimap (and staying out of combat ... don't get chased), and waiting approximately 30 seconds.

You can also change stance while in combat if you have an Armory imprinted with a different stance. You should get a free Armory when you complete the mission to place items in your base at level 8 or 9. You can purchase more Armories from the Marketplace. When using an Armory in combat, however, it locks you from using the in-combat armory switch for a set amount of time, indicated by an icon under your player frame.