Retrain a pybrain neural network after adding to the dataset
It dependes of what is your objective. If you need an updated NN-model you can perform an online training, i.e. performing a single step of back-propagation with the sample acquired at time $t$ starting from the network you had at time $t-1$. Or maybe you can discard the older samples in order to have a fixed amount of training samples or you can reduce the size of the training set performing a sort of clustering (i.e. merging similar samples into a single one). 
If you explain better your application it'd be simpler suggesting solutions.
I have a pybrain NN up and running, and it seems to be working rather well. Ideally, I would like to train the network and obtain a prediction after each data point (the previous weeks figures, in this case) has been added to the dataset.
At the moment I'm doing this by rebuilding the network each time, but it takes an increasingly long time to train the network as each example is added (+2 minutes for each example, in a dataset of 1000s of examples).
Is there a way to speed up the process by adding the new example to an already trained NN and updating it, or am I overcomplicating the matter, and would be better served by training on a single set of examples (say last years data) and then testing on all of the new examples (this year)?