When Adam runs out of air I see one of three things happening:

1. He just continues to be alive without oxygen. That would be an extrapolation of his power not previously shown. But if so, would he be alive as if he could breathe or alive as someone unable to breath, which is painful.

2. He dies and stays dead until oxygen is available. This raises the question of decay and whether it can happen to him. This would seem the logical result since Claire stayed dead after the car accident until the mechanism of death (the shrapnel in her head) was removed. But in other examples of the power the body has physically rejected the cause of death so that it could come back to life.

3. He dies of asphyxiation. His power returns him to life and he
immediately begins asphyxiating again. Only to return to life and do it again. The pain, repeated, every few minutes in a completely dark claustrophobic environment until someone finds him and releases him. This is the darkest of the three options and would seemingly result in insanity, but one wonders if his power can cure that as well. If so, that would be one uber pissed Adam at the other end.

There is also the matter of starvation/dehydration to consider. Can Adam starve to death?

Mama Petrelli made it clear to Matt that neither Adam or Peter would really die unless unless he put a bullet through their heads. If you consider Peter and Claire's previous brushes with death...car accident, autopsy, glass in the head...I would assume he'd bounce back once air is re-introduced.

On thing that I never saw hinted at in either of the last two episodes are the potential side effects for using Claire's blood for regeneration. Sylar eats brains for his power, Peter absorbs his by being near other heroes, but why doesn't Nathan or Noah absorb Adam and Claire's powers after receiving their blood?

It turns out he keeps dying, revives, and dies again. Also, someone is out there looking for him.