I have the same problem here. When I used pack_padded_sequence, sum of some gradients is zero. So I decide to  use padding without pack, but the gradients of layers is about 10^8, and sum of the first weights(rnn.weight_ih_l0) == 0. Did you already find a solution?
Optimzer = Adam
Loss = CrossEntropy
Learning_Rates = 0.1 - 0.001
Batch_size = 10 - 40
Total Samples to train = 1100