No healing item can heal multiple times. My Weavile BB'ed, and it appeared that he was dead (his ENTIRE health bar disappeared), but then he Dark Voided (it missed). Next turn, he has 2/3 life back, with no message from the game. He then Dark Voids me, and fails to kill my Weavile for 4 turns (lol), at which point I wake up, Brick Break, and right before his health bar depletes, he suddenly has full health. His bar is depleted to 1/4 of its life, where it's revealed that my Brick Break was a CRITICAL HIT. A standard CB Weavile Brick Break to a Darkrai has ~45% chance of OHKOing. And given how slowly the bar depleted, it felt like he had more HP than a Blissey. And after waiting a minute or so, I suddenly get a connection error. Strange, eh?
EDIT: From what I saw, the Darkrai ran Dark Void/ Dark Pulse/ Dream Eater/ Something else. Darkrai attacked every turn, either Dream Eating (to no avail) or Dark Pulsing. He had no opportunity to heal.