Should a model be re-trained if new observations are available?
When new observations are available, there are three ways to retrain your model:


Online: each time a new observation is available, you use this single data point to further train your model (e.g. load your current model and further train it by doing backpropagation with that single observation). With this method, your model learns in a sequential manner and sort of adapts locally to your data in that it will be more influenced by the recent observations than by older observations. This might be useful in situations where your model needs to dynamically adapt to new patterns in data. It is also useful when you are dealing with extremely large data sets for which training on all of it at once is impossible.
Offline: you add the new observations to your already existing data set and entirely retrain your model on this new, bigger data set. This generally leads to a better global approximation of the target function and is very popular if you have a fixed data set, or if you don't have new observations to often. However it is unpractical for large data sets.
Batch/mini batch: this is sort of a middle ground approach. With batch, you wait until you have a batch of $n$ new observations and then train your already existing model on this whole batch. It is not offline as you are not adding this batch to your preexisting data set and then retraining your model on it and it is not online as your are training your model on $n$ observations at once and not just a single one. So it's a bit of both :) Mini batch is exactly the same except that the batch size is smaller so it tends towards online learning. Actually online learning is just batch with batch size 1 and offline is batch with batch size the size of the whole data set. 


Most models today will use batch/mini batch and the choice for the size of the batch depends on your application and model. Choosing the right size batch is equivalent to choosing the right frequency with which to re-train your model. If your new observation have a low variance with your existing data, I'd suggest larger batches (256-512 maybe) and if on the contrary new observations tend to vary greatly with your existing data, use small batches (8-256). At the end of the day, batch size is kind of like another hyper-parameter which you need to tune and which is specific to your data