Problem of continuous training - Supervised learning
What you are describing is called auto-adaptive learning. This is what most recommendation systems use to adapt to ever changing data and feedback. It is also known as autoML.
This https://towardsdatascience.com/how-to-apply-continual-learning-to-your-machine-learning-models-4754adcd7f7f
Article does a good job of explaining it. Based on what your data looks like, you might have to choose the appropriate retraining strategy and do a staggered deployment.