There are two outcomes to leaving the battle depending on your actions:
If it happened by accident, or you lost connection, BUT managed to reconnect on time, the battle continues. Obviously your enemy would have pushed you very hardly, but you may still have a chance. The game restarted on me once, but I managed to return on time, and TIE it.
IF you leave the battle intentionally at any point, without going back - The battle continues and you'd lose however crows the enemy manages to destroy, and however many trophies you were supposed to lose. I've left once or twice, seeing the enemy is the taunt-type and didn't want to give him the pleasure of taunting me while waiting for the OK button, i simply left few seconds before the time expired.
There are no repercussions or penalties other than the lose, that would have happened with or without you. The game is single player and you leaving would only penalize you, thus no need for punishment like cool-down or something similar.