I apologise for the confusion. To get Break HP Limit you need the Enterprise. To obtain this accessory you need to ensure you miss out the mission "Shave the Hypello" in Chapter 1. In Chapter 2, just before Yuna dances on the roof of the Celsius, Tobli will appear with the other musicians in the corridor. Push Tobli into the lift first, followed by the trumpet player, then the harp player, then the drummer (their names evade me).
A chocobo can be used more than once as long as it is has gained a level. You cannot send out the same chocobo 5 times, then level it up and send it out again.
