Is this a correct way improving a statistical model?
No offense, but let me guess, you work for a large company where there is no person with a full understanding of the process overseeing this? I say this because it sounds as if the testers want you to manually and intentionally over-fit your models. There is no such thing as a perfectly accurate model.

Yes, I would say that there is bias in your model building. New model input should be a random selection not by finding and labeling similar instances to ones that were misclassified.

Your production model will degrade over time (the distribution in the population has changed). You should have a sense of a threshold, an error rate at which is no longer exceptable and you will need to retrain. To retrain, you could add a random selection of new labeled data to your existing data, then train, validate, select model, deploy, and monitor. 

You may "fix" an error report with a new retraining, but it is an unrealistic expectation that this will also cover all previous error reports. Your model needs to generalize. See here:

https://en.wikipedia.org/wiki/Test_set

Look at the image at the bottom. In essence you are being asked to create the orange model were you want to create the green model, which generalizes better to unseen data.