Why does a binary Keras CNN always predict 1?

I want to build a binary classifier using a Keras CNN. I have about 6000 rows of input data which looks like this:

>> print(X_train[0]) 
[[[-1.06405307 -1.06685851 -1.05989663 -1.06273152]
  [-1.06295958 -1.06655996 -1.05969803 -1.06382503]
  [-1.06415248 -1.06735609 -1.05999593 -1.06302975]
  [-1.06295958 -1.06755513 -1.05949944 -1.06362621]
  [-1.06355603 -1.06636092 -1.05959873 -1.06173742]
  [-1.0619655  -1.06655996 -1.06039312 -1.06412326]
  [-1.06415248 -1.06725658 -1.05940014 -1.06322857]
  [-1.06345662 -1.06377347 -1.05890365 -1.06034568]
  [-1.06027557 -1.06019084 -1.05592469 -1.05537518]
  [-1.05550398 -1.06038988 -1.05225064 -1.05676692]]]
>>> print(y_train[0])
[1]

And then I've build a CNN by this way:

model = Sequential()
model.add(Convolution1D(input_shape = (10, 4),
                        nb_filter=16,
                        filter_length=4,
                        border_mode='same'))
model.add(BatchNormalization())
model.add(LeakyReLU())
model.add(Dropout(0.2))

model.add(Convolution1D(nb_filter=8,
                        filter_length=4,
                        border_mode='same'))
model.add(BatchNormalization())
model.add(LeakyReLU())
model.add(Dropout(0.2))

model.add(Flatten())

model.add(Dense(64))
model.add(BatchNormalization())
model.add(LeakyReLU())

model.add(Dense(1))
model.add(Activation('softmax'))

reduce_lr    = ReduceLROnPlateau(monitor='val_acc', factor=0.9, patience=30, min_lr=0.000001, verbose=0)

model.compile(optimizer='adam', 
              loss='binary_crossentropy',
              metrics=['accuracy'])

history = model.fit(X_train, y_train, 
          nb_epoch = 100, 
          batch_size = 128, 
          verbose=0, 
          validation_data=(X_test, y_test),
          callbacks=[reduce_lr],
          shuffle=True)

y_pred = model.predict(X_test)

But it returns the following:

>> print(confusion_matrix(y_test, y_pred))
[[  0 362]
 [  0 608]]

Why all predictions are ones? Why does the CNN perform so bad? Here are the loss and acc charts:

It always predicts one because of the output in your network. You have a Dense layer with one neuron, with a Softmax activation. Softmax normalizes by the sum of exponential of each output. Since there is one output, the only possible output is 1.0.

For a binary classifier you can either use a sigmoid activation with the "binary_crossentropy" loss, or put two output units at the last layer, keep using softmax and change the loss to categorical_crossentropy.