Are the robots we create alive?
You're implying that something has to have a physical presence to be considered alive. Whether something is physical or virtual doesn't affect its state of order.
The robots, in a way, do repair themselves by hitting the opponent and getting the energy bonus. It is impossible for them to "reproduce" in the sense of creating new robots in the middle of a battle. Their existence prevails as long as they kill the enemy and avoid getting killed themselves.