What is the main weakness of a zoolock-deck?

Nowadays many players across all ranks seem to play a zoolock-deck. The concept behind this deck is just overrunning your oppenent with low-mana-minions in the early game and then finishing him off with a doomguard or leeroy. As a warlock can lifetap nearly every turn, he always has twice as much cards as every other class, so he does never run out of cards (even if he plays card-burn-cards like soulfire or doomguard).

For me it seems like this is a deck without a major weakness, but I think/hope that I am overseeing something. So my question is: What is the main weakness of such an aggressive rush-deck (besides from maybe facing another zoolock)?