Asthma is a complex chronic inflammatory disease of the small airways that has dramatically increased in prevalence in the industrialized countries during the last decades. Risk factors for adult asthma have been related to the complex array of gene-environment interactions and exposure of the immune system to allergens in early childhood. In genetically predisposed subjects, continuous exposure to environmental agents such as allergens or infections can lead to recurrent airway symptoms characterized by recurrent episodes of airway inflammation and bronchoconstriction with clinical symptoms of cough, dyspnea or wheezing. Here we report that the long term temporal dynamics of recurrent airway symptoms in a population of unselected infants display a complex intermittent pattern and the distribution of inter-episode intervals follows a power law. We interpret the data using a model of the dynamics of attack episodes in which an attack is triggered by an avalanche of airway constrictions. We map the dynamics of this model to the known problem of a random walk in the presence of an absorbing boundary in which the walker corresponds to the fluctuations in contractile state of airway smooth muscle cells. These findings may provide new insight into the mechanisms of otherwise unexplained symptom episodes.