The alkalosis persists as long as the initiating disorder persists unless some other disorder or complication causing impairment of the hyperventilation intervenes. For example, a hyperventilating head injury patient may develop acute neurogenic pulmonary oedema and this complication would tend to cause the arterial pCO2 to rise.
This is different to the situation with a metabolic alkalosis where maintenance of the disorder requires an abnormality to maintain it as well as the problem which initiated it.
A patient cannot have both a respiratory alkalosis and a respiratory acidosis. There may of course be multiple factors acting to alter an individual's alveolar ventilation but each of these various factors are not considered separate respiratory acid-base disorders. Essentially this is because a person cannot be both hyperventilating and hypoventilating at the same time.
Using the above hyperventilating head injured patient example: This patient has a neurogenic cause for hyperventilation and if the arterial pCO2 is lowered, then she is said to have a respiratory alkalosis. If neurogenic pulmonary oedema develops subsequently and decreases alveolar ventilation to normal and returns arterial pCO2 to 40mmHg (assuming no metabolic acid-base disorders are present), then she now has no respiratory acid-base disorder.
The above respiratory situation is different to that occurring with a metabolic disorder. A patient can have a lactic acidosis and then develop a metabolic alkalosis (eg due to vomiting) and end up with a HCO3 level & pH which are normal. This is possible if the acidosis and the alkalosis exactly balance each other. This patient is then said to have both a metabolic acidosis AND a metabolic alkalosis. It is therapeutically useful to know this rather then to say there is no acid-base disorder present.