The main drawbacks with Neural Networks (NNs) are complexity (i.e. "black-box" model as Dr. Mandal has mentioned), and also that a large dataset is often needed to train and initialise the model properly. NN models, if correctly implemented, can have excellent performance for pattern recognition. However they are not widely used in power applications outside of academia, and I don't know of any utilities that are currently using NN's for voltage stability assessment.