The flying adrenaline staff is a good combo, but it doesn't really leave room in your deck for much of anything else. Therefore, it's quite easy to completely shut down. Try playing adrenastaves against almost any shield, or against eternity/rewind, or lobotomy, or things like that, and you'll see what I mean. A 2 damage reduction shield will wreck this deck, rewind will cost you an adrenaline and a flying weapon and set you back a turn, and lobotomy will remove the healing, which is the only thing the deck has going for it. Even if you need to use two cards to destroy one adrenastaff, like two shockwaves or two thunderbolts, the other guy still has card advantage since three cards are invested in one adrenastaff.
edit: it does occur to me that this is slightly inconsistent with some other game behaviour, specifically adrenaline on pests or scorpions (all types) in that only every second hit will drain quanta or poison, whereas with adrenastaves, every hit heals you.