weight training speed too slow in CNNs
In machine learning, the vanishing gradient problem is a difficulty
  found in training artificial neural networks with gradient-based
  learning methods and backpropagation. In such methods, each of the
  neural network's weights receives an update proportional to the
  partial derivative of the error function with respect to the current
  weight in each iteration of training. The problem is that in some
  cases, the gradient will be vanishingly small, effectively preventing
  the weight from changing its value. In the worst case, this may
  completely stop the neural network from further training.


Source :: https://en.wikipedia.org/wiki/Vanishing_gradient_problem

Thus, gradient is vanishing till it reaches initial layer of neural network and in turn very little change in weights.