Like with all legendary and interactible Pokemon, if you get team wiped, run, or faint it, it will reappear at its location/go back to roaming the wild once you challenge and defete the league. (It doesn't matter whether it's the first time, or a subsequent challenge, this maniac always comes into play unless you've captured the Pokemon or the event has expired.) This is what happened for you to have the chance to capture Kyurem in the first place.
Source: Knowledge/experience.
