When a new battle begins in the Thorn arena the combatants do not engage at times. Red Lucy will not interact with you until a match ends making it impossible to complete her quests.
I left the arena and came back several hours later, the two cazadors were still there faced off but not fighting. This happened with other combatants as well. Some froze back in the cage. I also exited the game and restarted it. They were still not engaging combat.
I tried jumping into the arena to try to trigger them to attack me. Not only did that NOT work, everyone in the Thorn opened fire on me, Boone and ED-E went berzerk firing on everything and of course... I died.
I tried exiting and restarting the game, but they did not 'unstick." Finally, I resolved the issue by opening the console, selecting each combatant and doing a "kill" command on them. The gates closed and Red Lucy was approachable.
Please note that this seemed to happen only about 20% of the time. Other matches ran fine.

Same problem here: two radscorpions staring at each other. Same solution - use console to kill one of them.