Incremental learning with new samples
This is what Machine Learning models are used for..(to predict what they think will happen in the near time based on the data they have been fed into....)

A simple answer is this 

The first couple days of data are the most important , you need to gauge and have a watch over your model..

As with any incremental learning, you can learn more recent stuff but also underfit the past significantly more than without learning the new stuff.
Therefore, it's why there's a monitoring to perform on models which use incremental learning (especially on production systems).

Provided that other things remains similar with time..(same Preprocessing, same scaling etc..)

But let's say if you have tons of data everyday, then nearly at the month end, the model can be completely trained on the last months data or else checkpoints needs to be kept