Machine Learning models in production environment

Lets say a Model was trained on date $dt1$ using the available labeled data, split into training and test i.e $train_{dt1}$, $test_{dt1}$. This model is then deployed in production and makes predictions on new incoming data. Some $X$ days pass, and there is bunch of labelled data that is collected in between $dt1$ and $dt1 + X$ days, lets call it $Data_x$. In my current approach, I take random samples out of $DATA_x$ (take for e.g 80/20 split) ,

So, $80\%$ of $DATA_x$ = $train_x$ (new data used to fine-tune the existing model trained on $dt1$) $20\%$ of $DATA_x$ = $test_x$ (new data added to the $test_{dt1}$)

This process of fine-tuning repeated as time passes.

By doing this I get an ever expanding test set, as well as I prevent retraining the whole model (essentially I can throw away the old data as the model has learnt from it). The new model generated is just a fine-tuned version of the old one.

I have some questions, regarding this approach:

1. Are there any obvious drawbacks in doing this?
2. Would the model ever need to be completely retrained (forgetting everything that was learnt before, and training the model with new train/test splits ) after some time or can the approach I described above continue indefinitely ?
3. What should be the condition for swapping the existing deployed model with the newly fine-tuned model ?