For time series forecasting, as you've seen too short and the model forecast will drift over time. Too long, and the model may be more accurate over the long term, but not as high in the short term. So yes, the "window" length of data you use to train is important.
However, it isn't the only thing to consider. On top of the "window" that you train, you also need to determine how often you want to retrain the data. For real time data, this is a must. I.e. at some period of time, you retrain the model based on the new data, usually at the same window length, and then compare the models performance to the one you've already trained. If it's better, then replace the existing, if it isn't keep the existing.