How long does someone in a state of asthmaticus and respiratory failure have before brain damage occurs?

Depends...: The answer depends on the person's oxygen level during the episode. If the oxygen level is maintained, then the brain will be undamaged. Whether or not brain damage occurs depends on how low the oxygen level in the blood becomes; the lower the oxygen level, the less time it takes for brain damage to occur. The time can be measured in minutes if there is little to no oxygen getting to the brain.

Depends on O2 level: Brain damage can only occur if o2 transport is impaired and to a significant degree. Generally a o2 saturation less than 80 percent for longer than 30 minutes can produce transient or permanent cognitive effects. As the o2 saturation becomes lower the risk becomes greater and duration even shorter to cause damage.