There are multiple reasons. The main issue has to do with validation error. It usually follows a U curve, with a minimum at some epoch. This is the point at which we usually stop the training (`early stopping`). Any further training, with or without new data is only going to make the performance worse (I don't have a paper to cite for that).

I also started with the best model and that did not work. But when I took the model 2 epochs before the best model, it worked well. In my case(speech recognition), it was a nice balance between improvement and training time.