The problem in your case (as I thought previously) is the sigmoid activation function. It suffers from many problems. Out of that your performance decrease is likely due to two reasons:
NOTE: The link provided for 'Vanishing Gradient' explains beautifully why increasing layers make your network more susceptible to saturation of learning.
The vanishing gradient problem makes sure your Neural Neyt is trapped in a non optimal solution. While the high learning rate ensures that you get trapped in the non optimal solution. In short the high learning rate after a few oscillations will push your network to saturation.
Solution:
- Best solution is to use the ReLu activation function, with maybe the last layer as sigmoid.
- Use an adaptive optimizer like AdaGrad, Adam or RMSProp.
- Decrease the learning rate to $10^-6$ to $10^-7$ but to compensate increase the number of epochs to $10^6$ to $10^7$.