The operation of stochastic neural networks with randomly disconnected or blanked out synaptic connections can optimize the power consumption of its circuit implementations in traditional crossbars. However, the permanent disconnection of some synaptic weights can lead to the poor performance of the network, which will require further optimization of the remaining active synapses. In this work, we propose a learning scheme for such stochastically blanked out neural networks. The architecture of the neural network is implemented with standard 0.18u CMOS circuits, in 1T1M crossbar configuration for controlling the blank out rate. The results of retraining the network with up to 50\% disconnected synapses are reported for the standard image classification problem of MNIST handwritten digits recognition.