Classification model not working for a large dataset

I’m working with an online retail order dataset consisting on 3 columns: Client ID, month of purchase and Product ID (one-hot encoded). Something like this:

My objective is to use this dataset to train a Keras classification model. While this approach shows good results when using a very small sample of the dataset (e.g: 5-10 rows), the model does not converge when larger samples are used (e.g: 100-200 rows) or the full dataset (around 540k rows). This is my Python code:

model = Sequential()
model.add(Dense(units=64, activation='relu', input_dim=2))
model.add(Dense(units=saidas_units, activation='softmax'))
model.compile(loss='categorical_crossentropy',
              optimizer='sgd',
              metrics=['accuracy'])
model.fit(myInputs, myProducts,
      batch_size=10,
      epochs=2000,
      verbose=1,
      validation_data=(myInputs, myProducts))

Weirdly enough, in some cases even though the "loss" value is low and the "accuracy" value is high, the product predictions produced by the model are always the same, no matter the inputs (clientId/month).