Can Convolution neutral network train(learn) separately (train different times)?
This is called curriculum learning , and not only this approach is possible but also it is shown to be quite effective.
A few years ago I also came up with similar idea. Basically the idea is, instead of flooding the network with different examples, we can categorize the training data from simple to hard and gradually feed data ordered based on difficulty. 
After searching for a while, I encountered this paper by Yoshua Bengio, which i think is among the important ones on curriculum learning. Also check out 
FlowNet 2.0 which is a network trained with this approach.