How long can an average aerobatic plane sustain 0g?
An aerobatic aircraft (as well as any aircraft) can sustain 0g until the pilot pulls up, the aircraft hits the ground, or reaches terminal velocity. 

In order to sustain 0g  the aircraft must be accelerating towards earth at $9.8 m/s^2$ (meters per second squared). That means there isn't much time before the aircraft reaches its maximum speed. Once the aircraft can no longer accelerate at the same rate of gravity, then the occupants will no longer feel 0g. In sky diving (and physics) this is called terminal velocity, which is the velocity at which air friction prevents the object from falling any faster. 

Acceleration is change in speed, so naturally you don't have to be going straight down to be accelerating towards the earth (we're talking about vertical speed). If you are going up at 200kts and begin to decelerate at exactly $9.8m/s^2$ you will "feel" like you are in 0g (free fall) even though you are continuing to go up for a few seconds. But this will only last for a few seconds before the aircraft momentarily reaches its apex and you and the aircraft begin moving towards the earth. If the aircraft can match exactly the acceleration of gravity, then you will continue to feel weightless (i.e. 0g).

But you can't continue to accelerate indefinitely towards earth without either reaching terminal velocity or exceeding the aircraft's maximum speed. So the limit of the sustained 0g flight is the pilot pulling back on the yoke and climbing to prevent the destruction of the aircraft and death of all on board. 

However, even if the wings broke off of the airplane, and you were plummeting towards the ground in the fuselage of the aircraft, you would only remain weightless so long as the fuselage continued to accelerate towards the earth at $9.8m/s^2$. At some point, if you had enough altitude, the drag (wind friction) on the fuselage would prevent it from continually accelerating towards earth and you would reach an equilibrium speed where the force of gravity equals the force of drag and you would no longer feel 0gs.