Real-time anomaly detection from time series data
I think you are using batch processing model(you didn't using any real-time processing frameworks and tools) so there shouldn't be any problem when making your model or classification. The problem may occur a while after you make model, so after that time your predicted model is not valid.
I suggest some ways maybe solve this problem:
Use Real-time or near real-time processing(like apache spark, flink, storm, etc).
Use some conditions to check your data periodically for any changes if any change happens run your model again.
Delete instances that you think they may cause problem(may that changed data known as anomaly itself) but before make sure that data is not so important.
Change you algorithm and use algorithms that not very sensitive to changes.
I have some problem when detecting anomaly from time series data. 
I use LSTM model to predict value of next time as y_pred, true value at next time of data is y_real, so I have er = |y_pred - y_t|, I use er to compare with threshold = alpha * std and get anomaly data point. But sometime, our data is effected by admin or user for example number of player of a game on Sunday will higher than Monday. 
So, should I use another model to classify anomaly data point or use "If else" to classify it?