A significant part of using a neural network is training it. Training is an iterative process where the data is repeatedly presented to the network and it incrementally improves its model to match the data more closely. Training is difficult because it can be computationally expensive and there are several parameters which must be adjusted in order to get it to learn well. The concept of training is somewhat foreign to memory based learning. Its training phase consists only of storing all the data its given.
The training required for neural nets presents an additional problem for them. In order to do feature selection, adjust and test different network architectures, and validate the learned model, it may be necessary to train several different networks on several different sets of data. The computation time required for training restricts the amount of testing that can be done with a neural net, while a memory based learner doesn't require any new training to test different subsets of data and different models.