Step 1: This is a negative question, so confirm what truly belongs to ABPA and discard the odd one out.
Step 2: ABPA is an allergic, IgE-driven reaction to Aspergillus in asthmatic airways. Expected findings are very high serum IgE, fleeting pulmonary infiltrates, blood eosinophilia, central bronchiectasis, positive skin tests and precipitins, and it can arise in lungs bearing old cavities.
Step 3: Recurrent pneumonia is not part of the classic ABPA picture, which is hypersensitivity rather than repeated infection. Hence the feature not seen is recurrent pneumonia.
\[\boxed{\text{Recurrent pneumonia}}\]