Food allergy is usually difficult to diagnose in early life, and the inability to diagnose patients with atopic diseases at an early age may lead to severe complications. Numerous studies have suggested an association between the infant gut microbiome and development of allergy. In this work, we investigated the capacity of Long Short-Term Memory (LSTM) networks to predict food allergies in early life (0-3 years) from subjects' longitudinal gut microbiome profiles. Using the DIABIMMUNE dataset, we show an increase in predictive power using our model compared to Hidden Markov Model, Multi-Layer Perceptron Neural Network, Support Vector Machine, Random Forest, and LASSO regression. We further evaluated whether the training of LSTM networks benefits from reduced representations of microbial features. We considered sparse autoencoder for extraction of potential latent representations in addition to standard feature selection procedures based on Minimum Redundancy Maximum Relevance (mRMR) and variance prior to the training of LSTM networks. The comprehensive evaluation reveals that LSTM networks with the mRMR selected features achieve significantly better performance compared to the other tested machine learning models.