Neural Network Normalization and de-Normalisation of data
You should definitely not be storing new max/mins after training is finished since that will mess up the values for the values that are within the old max and min.

You're network might not do very well on any of these new values anyway since they are more extreme than anything it saw during training. You should scale everything using the max/min you found during training. You could cap anything more extreme than that to be either 0 or 1.